library(readxl)
telecom <- read_excel("~/Telco-customer-churn.xlsx")
str(telecom)
## tibble [999 × 5] (S3: tbl_df/tbl/data.frame)
##  $ Churn         : chr [1:999] "No" "No" "Yes" "No" ...
##  $ SeniorCitizen : num [1:999] 0 0 0 0 0 0 0 0 0 0 ...
##  $ tenure        : num [1:999] 1 34 2 45 2 8 22 10 28 62 ...
##  $ MonthlyCharges: num [1:999] 29.9 57 53.9 42.3 70.7 ...
##  $ TotalCharges  : num [1:999] 29.9 1889.5 108.2 1840.8 151.7 ...
attach(telecom)
#Get the Correlations between the measurements
cor(telecom[-1])
##                SeniorCitizen      tenure MonthlyCharges TotalCharges
## SeniorCitizen     1.00000000 -0.02896797      0.1819430   0.05224135
## tenure           -0.02896797  1.00000000      0.2497981   0.83653519
## MonthlyCharges    0.18194300  0.24979805      1.0000000   0.63523217
## TotalCharges      0.05224135  0.83653519      0.6352322   1.00000000
# Using prcomp to compute the principal components (eigenvalues and eigenvectors). With scale=TRUE, variable means are set to zero, and variances set to one
telecom_pca <- prcomp(telecom[,-1],scale=TRUE)
telecom_pca
## Standard deviations (1, .., p=4):
## [1] 1.4794627 1.0353363 0.8241061 0.2451901
## 
## Rotation (n x k) = (4 x 4):
##                       PC1         PC2         PC3          PC4
## SeniorCitizen  0.08960417 -0.88666415  0.45354733  0.009623196
## tenure         0.56498847  0.31234448  0.51103948 -0.567509999
## MonthlyCharges 0.48563207 -0.32776108 -0.72919909 -0.353557414
## TotalCharges   0.66099970  0.09402283  0.03744529  0.743530060
summary(telecom_pca)
## Importance of components:
##                           PC1    PC2    PC3     PC4
## Standard deviation     1.4795 1.0353 0.8241 0.24519
## Proportion of Variance 0.5472 0.2680 0.1698 0.01503
## Cumulative Proportion  0.5472 0.8152 0.9850 1.00000
# sample scores stored in telecom_pca$x
# singular values (square roots of eigenvalues) stored in sparrow_pca$sdev
# loadings (eigenvectors) are stored in telecom_pca$rotation
# variable means stored in telecom_pca$center
# variable standard deviations stored in telecom_pca$scale
# A table containing eigenvalues and %'s accounted, follows
# Eigenvalues are sdev^2
(eigen_telecom <- telecom_pca$sdev^2)
## [1] 2.18880975 1.07192119 0.67915089 0.06011817
names(eigen_telecom) <- paste("PC",1:4,sep="")
eigen_telecom
##        PC1        PC2        PC3        PC4 
## 2.18880975 1.07192119 0.67915089 0.06011817
sumlambdas <- sum(eigen_telecom)
sumlambdas
## [1] 4
propvar <- eigen_telecom/sumlambdas
propvar
##        PC1        PC2        PC3        PC4 
## 0.54720244 0.26798030 0.16978772 0.01502954
cumvar_telecom <- cumsum(propvar)
cumvar_telecom
##       PC1       PC2       PC3       PC4 
## 0.5472024 0.8151827 0.9849705 1.0000000
matlambdas <- rbind(eigen_telecom,propvar,cumvar_telecom)
rownames(matlambdas) <- c("Eigenvalues","Prop. variance","Cum. prop. variance")
round(matlambdas,4)
##                        PC1    PC2    PC3    PC4
## Eigenvalues         2.1888 1.0719 0.6792 0.0601
## Prop. variance      0.5472 0.2680 0.1698 0.0150
## Cum. prop. variance 0.5472 0.8152 0.9850 1.0000
summary(telecom_pca)
## Importance of components:
##                           PC1    PC2    PC3     PC4
## Standard deviation     1.4795 1.0353 0.8241 0.24519
## Proportion of Variance 0.5472 0.2680 0.1698 0.01503
## Cumulative Proportion  0.5472 0.8152 0.9850 1.00000
telecom_pca$rotation
##                       PC1         PC2         PC3          PC4
## SeniorCitizen  0.08960417 -0.88666415  0.45354733  0.009623196
## tenure         0.56498847  0.31234448  0.51103948 -0.567509999
## MonthlyCharges 0.48563207 -0.32776108 -0.72919909 -0.353557414
## TotalCharges   0.66099970  0.09402283  0.03744529  0.743530060
print(telecom_pca)
## Standard deviations (1, .., p=4):
## [1] 1.4794627 1.0353363 0.8241061 0.2451901
## 
## Rotation (n x k) = (4 x 4):
##                       PC1         PC2         PC3          PC4
## SeniorCitizen  0.08960417 -0.88666415  0.45354733  0.009623196
## tenure         0.56498847  0.31234448  0.51103948 -0.567509999
## MonthlyCharges 0.48563207 -0.32776108 -0.72919909 -0.353557414
## TotalCharges   0.66099970  0.09402283  0.03744529  0.743530060
## Sample scores stored in sparrow_pca$x
telecom_pca$x
##                  PC1           PC2           PC3           PC4
##    [1,] -2.015467453  0.3063516984  0.0120502201  0.3952287653
##    [2,] -0.286167867  0.5013439720  0.0615892254 -0.0753083935
##    [3,] -1.580345244  0.0591421382 -0.5512321189  0.1140939064
##    [4,] -0.287614123  0.7983943370  0.6445959152 -0.1696250516
##    [5,] -1.294160708 -0.1237314581 -0.9613547414 -0.0709556042
##    [6,] -0.494044929 -0.3379468993 -1.5326506543 -0.3329395336
##    [7,] -0.020111087  0.0003749667 -0.9685190929 -0.1613687025
##    [8,] -1.733455753  0.4319562059  0.2043525014  0.2789892675
##    [9,]  0.688536938 -0.0510378498 -1.2097481522 -0.1275878542
##   [10,]  0.800699638  0.9284002528  0.6841006823 -0.1865781716
##   [11,] -1.254566657  0.2600970846 -0.2216823424  0.0644229830
##   [12,] -1.764971394  0.6268866250  0.5916904672  0.2774977466
##   [13,]  2.061385552  0.4838318990 -0.4400631575  0.0956542225
##   [14,]  1.724378831  0.3072806955 -0.7177116306  0.0522494039
##   [15,]  0.527494462 -0.1112877649 -1.2945144595 -0.1843081668
##   [16,]  3.161504599  0.5720136417 -0.4917171390  0.4115436863
##   [17,] -0.716173101  1.0901673293  1.3032764892 -0.3397861962
##   [18,]  2.952410314  0.6478858084 -0.2992142283  0.2764189167
##   [19,] -1.254731788  0.1623572800 -0.4124580865  0.0517707540
##   [20,] -0.052469384 -0.0261847489 -1.0136995538 -0.1778530396
##   [21,] -1.611728253 -2.1930906514  0.9970540300  0.3085286329
##   [22,] -1.878281489  0.5620845058  0.4865222098  0.3184532575
##   [23,] -2.175779144  0.4122570318  0.2483958170  0.5067450736
##   [24,]  0.775447113  0.8376438460  0.5105457067 -0.1338228327
##   [25,]  0.410974980  0.7056174597  0.3236927933 -0.0983047154
##   [26,] -0.507827005  0.4543022412  0.0135374770 -0.0810125188
##   [27,]  1.525172980  0.3179618635 -0.6575552351  0.0560433902
##   [28,] -2.009683010  0.3025303719  0.0035222862  0.3912049809
##   [29,]  2.415256278  0.7991045643  0.1058810951  0.1186320774
##   [30,] -0.777763717  0.1696083634 -0.4906300199 -0.0370124895
##   [31,]  2.848230035 -1.6564358066  1.1668468777  0.2246353601
##   [32,] -0.641013427 -2.7867310927 -0.3417486462 -0.3284125213
##   [33,] -0.300560723  0.3117621795 -0.3071772993 -0.0288213652
##   [34,] -2.174952795  0.4117111280  0.2471775407  0.5061702472
##   [35,] -1.519177173 -2.2542318748  0.8606070875  0.2441480838
##   [36,]  2.827024440  0.7296306943 -0.1149545366  0.2914726586
##   [37,] -1.194294975 -0.0682028508 -0.8724635335 -0.0740242687
##   [38,]  0.756572527  0.5250342636 -0.0992482896 -0.0213891894
##   [39,]  0.995843188  0.0282164677 -1.1156929653 -0.1195278411
##   [40,] -0.372576730 -0.2687303412 -1.4222942619 -0.2876389053
##   [41,] -1.361697679  0.2221115384 -0.2755626470  0.1014410539
##   [42,]  1.595061949  0.9430453465  0.5533983805 -0.0736439939
##   [43,] -1.686527850  0.6235121074  0.5699017654  0.2630821071
##   [44,]  1.605413825  0.7377433815  0.1493460653 -0.0429488503
##   [45,] -0.714410979 -0.0113787300 -0.8552542721 -0.1177632548
##   [46,]  1.086026186  0.4712426940 -0.2680799863 -0.0881353262
##   [47,] -1.658263057  0.1090959181 -0.4392579796  0.1648477748
##   [48,] -1.134762350 -0.2330839393 -1.2040775207 -0.1910210350
##   [49,]  1.167167537  0.5738663650 -0.0853678670  0.0005600547
##   [50,]  1.311538924  0.9603726853  0.6458001905 -0.1921306285
##   [51,]  1.264868979 -2.0625593971  0.6907915360 -0.0149786634
##   [52,] -0.168370241 -0.2188635628 -1.3651104889 -0.2895317085
##   [53,] -0.085154857 -2.1475877081  0.7917325457 -0.0363147592
##   [54,] -0.614912060 -2.5298658743  0.1513254615 -0.1432407568
##   [55,]  1.580551201 -1.6543390313  1.4266039081 -0.0209865789
##   [56,]  0.176758767 -2.5201212919  0.0148139888 -0.1829799378
##   [57,]  2.346069747  0.5803719891 -0.3096712143  0.1944602172
##   [58,]  3.020282165 -1.8392739689  0.7738886278  0.2966004227
##   [59,] -1.093507929  0.8111109188  0.8255104785 -0.0206660269
##   [60,]  3.124480162  0.6710979411 -0.2903972792  0.3974064804
##   [61,]  1.531689184  0.3036294823 -0.6862831312  0.0287731236
##   [62,]  1.870638938  0.6140627227 -0.1478439577  0.0985073036
##   [63,]  0.648254123  1.1866591365  1.2240615826 -0.4203028134
##   [64,] -0.961557792  0.2894863205 -0.2211229268  0.0176449277
##   [65,] -0.545892972 -0.2663085838 -1.3834428268 -0.2818011253
##   [66,] -1.169962034 -0.1577506121 -1.0513963954 -0.1181469042
##   [67,]  0.875427786  0.4968895086 -0.1769417601 -0.0595475609
##   [68,]  0.182493361  0.2447198211 -0.5327578437 -0.0720772747
##   [69,] -0.796456606  1.0666790373  1.2727579581 -0.3180565883
##   [70,] -0.750675757 -0.0930231842 -1.0075922102 -0.1228832013
##   [71,] -1.698149465  0.0967246467 -0.4557678685  0.1744954540
##   [72,] -0.700659398  1.0956912830  1.3104807748 -0.3148137478
##   [73,]  3.032428488 -1.8980463204  0.6562547371  0.3124827647
##   [74,] -0.313836135  1.1931437520  1.4280892831 -0.4804957131
##   [75,] -1.364614999 -0.0421342756 -0.7891642665 -0.0121639001
##   [76,]  2.554954116 -2.0261799036  0.5025524213  0.1964623697
##   [77,]  0.197136523  0.6995581852  0.3535888524 -0.0745083433
##   [78,] -1.322542296  0.1413066356 -0.4410049403  0.0890350495
##   [79,]  0.217664019 -2.1274182062  0.7726062771 -0.0961275654
##   [80,] -0.734366957  0.9524571386  1.0342366316 -0.1787310509
##   [81,] -1.197382016 -0.2340930443 -1.1940432895 -0.1738493029
##   [82,] -1.296764834  0.2274303565 -0.2778753067  0.0958974213
##   [83,] -1.008206279 -0.0953456690 -0.9611949560 -0.1256688903
##   [84,]  1.361647046  0.1888972503 -0.8759652645 -0.0193031968
##   [85,] -0.806959336  1.0558336138  1.2528522851 -0.2813738779
##   [86,] -0.448546799 -0.3174794868 -1.5019068907 -0.3197269722
##   [87,] -0.084717836  0.4703519543 -0.0392572419 -0.0536551817
##   [88,] -0.797431545  1.0412029346  1.2214304455 -0.2372032057
##   [89,] -0.891905672  1.0183499064  1.1951683772 -0.2254186136
##   [90,] -1.031259395  0.6564413875  0.5098277540  0.0270728460
##   [91,]  0.227101041  0.2038970410 -0.6216515858 -0.0591512269
##   [92,] -1.032457656 -2.5757692015  0.1430423631 -0.0944246254
##   [93,]  1.987686410  0.7651075091  0.1239313568  0.1167016622
##   [94,]  2.806811496  0.5133466217 -0.5333892179  0.2727432484
##   [95,]  2.903210552  0.7271987352 -0.1359404036  0.3470841182
##   [96,] -0.708173758 -0.0563325608 -0.9437915035 -0.1449897800
##   [97,]  1.543929464  0.9763055519  0.6292716107 -0.1089530202
##   [98,] -2.042972026  0.4566118480  0.3103904728  0.4350686525
##   [99,] -0.686131807  1.0897963793  1.2961226931 -0.3165244945
##  [100,]  0.606006347 -2.4340735414  0.0971351316 -0.1313806771
##  [101,] -2.174952795  0.4117111280  0.2471775407  0.5061702472
##  [102,] -2.187348029  0.4198996847  0.2654516848  0.5147926422
##  [103,]  0.918938002  0.2052854759 -0.7556317176 -0.0585346918
##  [104,]  0.828260114 -1.3164589611  2.2411930707 -0.2766375917
##  [105,]  3.004049207  0.5833891941 -0.4377168502  0.3807084725
##  [106,] -1.994145410  0.4204330920  0.2309257221  0.3922088180
##  [107,]  2.910881473  0.6851658542 -0.2177366027  0.2579300175
##  [108,] -1.044980444  0.7303122424  0.6580689327 -0.0255384601
##  [109,]  1.113535949  0.2883479476 -0.6316082014 -0.0625671835
##  [110,] -0.182569918  1.3696846049  1.7513460190 -0.6718857738
##  [111,]  1.806754913  0.4673260818 -0.4213335735  0.0630347745
##  [112,]  0.473311559  0.7644325971  0.4269041449 -0.1240317493
##  [113,]  1.079176733  0.3192866846 -0.5652398537 -0.0199814513
##  [114,]  0.624327885 -2.0273332320  0.8865403656 -0.0308186348
##  [115,]  0.802448837  0.9679188640  0.7620389149 -0.2349692600
##  [116,] -0.932457938 -0.3170301421 -1.4060826680 -0.2887548140
##  [117,] -0.881816122  0.7789851697  0.7217833082 -0.0630673719
##  [118,] -0.368163059 -0.3092994349 -1.5020791769 -0.3063862092
##  [119,] -1.021001971  0.9439411638  1.0735904064 -0.1492104927
##  [120,]  0.088899116  0.1143871675 -0.7671133245 -0.1638923674
##  [121,]  1.959011199  0.4578647766 -0.4705680350  0.0940391395
##  [122,] -2.026197593  0.4729935049  0.3395070540  0.4159711657
##  [123,] -1.188782751 -0.1484856985 -1.0296909860 -0.1122392064
##  [124,] -1.447591995  0.1665799333 -0.3674576470  0.1157125107
##  [125,] -2.083725783  0.4441172020  0.2938314490  0.4437406886
##  [126,]  0.539725647  0.1848646509 -0.7205916833 -0.0605840051
##  [127,]  0.209918439 -2.2003618683  0.6307395561 -0.0586370421
##  [128,] -0.010898566  1.3390376628  1.6560687648 -0.6036411741
##  [129,] -2.182389936  0.4166242621  0.2581420271  0.5113436842
##  [130,]  1.396133635 -1.3335566399  2.0941270073 -0.2082934779
##  [131,] -0.488380801 -0.1085994906 -1.0891420399 -0.1568600231
##  [132,] -0.576201423  0.3540315690 -0.1703852335 -0.0147272045
##  [133,]  0.757771042  1.0433573449  0.9199122068 -0.3088633185
##  [134,] -1.922916373  0.2452104750 -0.1243967224  0.3308482161
##  [135,] -1.742382162  0.1621482838 -0.3200446092  0.2176521793
##  [136,] -0.791376856  0.9282986842  0.9974460071 -0.1398480704
##  [137,] -0.275699196  0.1604626277 -0.6069323676 -0.0731386512
##  [138,] -0.376504769  1.2566716754  1.5656327046 -0.5261301134
##  [139,] -0.576670736  1.1707003910  1.4342995777 -0.3937585278
##  [140,] -1.102697315 -2.5293673802  0.2465958462 -0.0455643873
##  [141,]  2.637556123 -1.5669191859  1.3842277020  0.1888827841
##  [142,] -1.031083507 -0.0361726080 -0.8419731597 -0.0795512270
##  [143,]  2.224966267  0.5258663614 -0.3905755385  0.1131078737
##  [144,]  1.824074123  0.7191511070  0.0684508781  0.0206287085
##  [145,]  0.223919674 -1.0690561234  2.8500292312 -0.5490385180
##  [146,]  2.412380218  0.6164685312 -0.2521123012  0.1901086577
##  [147,] -2.127246954  0.4451612849  0.3036825113  0.4808911428
##  [148,] -1.754341192  0.1338461038 -0.3729250820  0.2135836445
##  [149,] -0.242980107  0.3699008128 -0.2042353704 -0.0598981756
##  [150,] -0.751647226  0.0909294433 -0.6492204286 -0.0550592777
##  [151,] -1.073099568 -0.0076498994 -0.7785687452 -0.0485870504
##  [152,] -0.640030879 -0.3063633944 -1.4425781495 -0.3087514494
##  [153,]  3.111701929  0.6419525586 -0.3461887078  0.4604697940
##  [154,]  1.786414072  0.6712071826 -0.0178471279  0.0211034744
##  [155,] -2.042218618  0.4839835491  0.3639012414  0.4280368175
##  [156,] -0.565777248 -0.0432490520 -0.9464418700 -0.1404773148
##  [157,] -0.137336369  0.0493816447 -0.8499160814 -0.1442996565
##  [158,] -1.581914961  0.6931113543  0.6875625870  0.1563249540
##  [159,] -0.827824399  0.1591071012 -0.5013908336 -0.0312876590
##  [160,] -1.813761641  0.4742723869  0.3022753840  0.3105090355
##  [161,] -1.105125107  0.2010771358 -0.3662922662  0.0504969156
##  [162,] -0.277685139  0.0339356276 -0.8522100655 -0.1525261096
##  [163,] -1.315154533 -0.1134487617 -0.9372422605 -0.0644836397
##  [164,]  1.019911639  0.6398949025  0.0736162178 -0.0375695116
##  [165,] -1.878916383  0.5420275733  0.4469341284  0.3421662599
##  [166,] -0.242720302  1.3264397073  1.6773555496 -0.6090995206
##  [167,] -1.210277456 -0.0957504472 -0.9230417556 -0.0796099086
##  [168,]  2.362522478  0.8075262451  0.1332558771  0.0954185136
##  [169,]  0.533272788 -1.4299135605  2.0763220454 -0.2129601398
##  [170,] -1.742987721  0.6107737100  0.5562482640  0.2586000645
##  [171,]  0.839076685  0.3833241167 -0.3916082964 -0.0674157512
##  [172,] -0.720591805 -0.4893079825 -1.7815320167 -0.4397049858
##  [173,] -0.540357577 -0.0535656476 -0.9715687177 -0.1434751867
##  [174,]  1.661339506  0.4531497085 -0.4201193144  0.0536221318
##  [175,] -1.279821564  0.8242893656  0.8876622997 -0.0008657922
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##  [407,]  2.064404873  0.5686455348 -0.2760269549  0.1509876815
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##  [432,]  1.550248609  1.0084496208  0.6906882065 -0.1006980939
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##  [437,] -1.164910240  0.8740599808  0.9638242302 -0.0746202140
##  [438,]  3.408500081  0.6245864092 -0.4400342944  0.5198183099
##  [439,]  0.638502621  0.2056759448 -0.6991462151 -0.0735459128
##  [440,] -1.598987594  0.0312161930 -0.6019610212  0.1055162942
##  [441,]  0.211180231 -0.3392982068 -1.6747279712 -0.3277936447
##  [442,]  1.941101101 -2.0601998743  0.5590539211  0.1147217859
##  [443,]  2.308994549  0.2919010370 -0.8650943459  0.1379217428
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##  [445,]  0.443198603  0.3126380992 -0.4517976587 -0.0574094940
##  [446,]  2.403876406  0.4776093588 -0.5224646571  0.2169309421
##  [447,] -1.359346405 -0.1270959033 -0.9552611401 -0.0611833419
##  [448,] -0.573228064  1.0521170270  1.2000464619 -0.3113763418
##  [449,] -0.591232088 -0.2867533777 -1.4141775823 -0.2948348188
##  [450,]  3.021994943  0.6830579553 -0.2455994728  0.3422993016
##  [451,] -0.197906966  1.2223658500  1.4618922107 -0.4606247013
##  [452,] -0.209341868 -2.1966241595  0.7204398777 -0.0380387927
##  [453,]  0.848218582  0.8627173863  0.5456990388 -0.1579850044
##  [454,]  0.066115975  0.1755639511 -0.6440909327 -0.1131558173
##  [455,] -0.336113247  1.1786331612  1.4037213320 -0.4615705502
##  [456,]  0.427460789 -0.1169553180 -1.2853346237 -0.2077174875
##  [457,]  0.415018801  0.0679562601 -0.9241517468 -0.0772211680
##  [458,]  0.148720263  0.2093340557 -0.5944646030 -0.1097096185
##  [459,] -2.150278386  0.4272261649  0.2729463859  0.4914460510
##  [460,] -1.267621674 -0.1876912229 -1.0904898064 -0.1249890647
##  [461,] -2.046673375  0.4840133358  0.3649139703  0.4245302034
##  [462,] -0.390588782  0.2271143799 -0.4537052794 -0.0838868528
##  [463,] -0.686440899 -0.4226232641 -1.6587452354 -0.4005008711
##  [464,] -0.556957327 -0.3582375903 -1.5593205729 -0.3597232511
##  [465,]  3.664449559 -1.7923804047  0.7339511122  0.5015545866
##  [466,]  0.522505972  1.1772706394  1.2301852470 -0.4030795561
##  [467,]  2.716104695 -1.8169864605  0.8787019765  0.2424903866
##  [468,]  2.469786466  0.8141590330  0.1228861750  0.1965185902
##  [469,] -0.955326849  0.9912891509  1.1542192917 -0.1982604541
##  [470,] -1.114668310  0.2003831248 -0.3655677951  0.0412665286
##  [471,] -1.471717864 -1.7714417761  1.7946903586  0.2617250699
##  [472,] -1.599813943  0.0317620968 -0.6007427449  0.1060911205
##  [473,] -1.025952606 -0.0114954697 -0.7945398509 -0.0891807614
##  [474,] -0.734317916  0.3885337095 -0.0721442981  0.0063462085
##  [475,] -1.274232466 -0.1833239927 -1.0807435962 -0.1203904541
##  [476,] -0.143678059  0.1189313633 -0.7129770338 -0.1310873587
##  [477,]  0.536500814 -2.0525579928  0.8543294070 -0.0190788094
##  [478,] -0.982752463 -0.0990229430 -0.9736689842 -0.1135848463
##  [479,] -0.726151046 -0.3519121990 -1.5139101565 -0.3417264690
##  [480,] -0.781912460  0.0932588786 -0.6382840532 -0.0740598282
##  [481,] -1.896698650  0.5521036461  0.4699634540  0.3507464167
##  [482,] -0.082609785  0.8158024990  0.6382360894 -0.1747758820
##  [483,] -0.028423837 -2.3448391950  0.3960366812 -0.0895563879
##  [484,]  3.184114370  0.6663115833 -0.3123208028  0.4343994170
##  [485,] -0.796080886 -0.1672797593 -1.1424023339 -0.1882858623
##  [486,]  2.252905439  0.8523075736  0.2421691834  0.1090109385
##  [487,] -0.154616411 -0.2308395468 -1.3908982002 -0.3056519804
##  [488,]  2.340036838  0.8102988297  0.1433678740  0.0836645424
##  [489,] -1.280016908 -0.1795026662 -1.0722156623 -0.1163666697
##  [490,]  2.512396435  0.5356958751 -0.4305530109  0.2266058228
##  [491,] -1.494985556  0.0029490050 -0.6767006534  0.0551632265
##  [492,] -1.237622292 -0.1647842795 -1.0517684192 -0.1186799220
##  [493,]  1.267859891 -1.5461613875  1.7014599257 -0.0962765962
##  [494,] -2.171647400  0.4095275129  0.2423044356  0.5038709419
##  [495,] -1.058855892  0.4543663216  0.1200718340  0.0346380592
##  [496,] -0.388707308  0.3782372678 -0.1600257651 -0.0185136216
##  [497,] -0.211680600  1.3415332719  1.7009548083 -0.6196723752
##  [498,] -1.676064236 -2.0162240967  1.3540320509  0.3791472849
##  [499,] -0.281294057 -0.2709420243 -1.4446207224 -0.2891167139
##  [500,]  1.257730880 -0.0658941382 -1.3513446892 -0.1228030889
##  [501,]  2.278696143 -1.5297894937  1.5305557843  0.0548529850
##  [502,]  1.434933438  0.9733438419  0.6455342650 -0.1334176019
##  [503,]  1.268504013  0.5312244136 -0.1884248203 -0.0148250648
##  [504,]  1.920925370  0.8440392592  0.2932045296  0.0330106199
##  [505,]  0.209019199 -2.4789164457  0.0894203126 -0.2030676589
##  [506,] -0.768218171 -0.0616194782 -0.9424670052 -0.1354517117
##  [507,] -0.907988452 -0.3806208401 -1.5340698833 -0.3436118700
##  [508,] -0.942389187 -0.1663238727 -1.1121416212 -0.1641028188
##  [509,] -2.180737238  0.4155324545  0.2557054746  0.5101940316
##  [510,]  0.222646044 -2.4796319030  0.0851319122 -0.1937568110
##  [511,]  2.407741051  0.4802126479 -0.5168510017  0.1562334800
##  [512,] -0.871838925 -2.5108722067  0.2382397447 -0.0972081984
##  [513,]  2.166835286  0.4124569284 -0.6017499108  0.1578198741
##  [514,]  0.518969956  0.0735808325 -0.9327752879 -0.1204672765
##  [515,]  1.275796804  0.1447137337 -0.9447518034 -0.0489658882
##  [516,] -0.565077168  0.4407247539 -0.0030253423 -0.0183301915
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##  [518,]  0.104039221 -2.1776060385  0.6968515989 -0.0919880235
##  [519,] -1.855949878  0.5619437973  0.4814618413  0.3360513707
##  [520,]  2.726633388  0.5956142245 -0.3563548668  0.2555524148
##  [521,] -0.374523696 -1.9138287633  1.3054844333 -0.0172428817
##  [522,]  1.472148386  0.5690059691 -0.1556439438  0.0251292071
##  [523,] -0.271709891  0.1530687225 -0.6218874377 -0.0867034619
##  [524,]  0.873523356  0.0944115336 -0.9632211678 -0.0675719682
##  [525,]  1.504387949  0.4692410532 -0.3572348641  0.0338841150
##  [526,]  3.657915782 -1.7893291126  0.7411715082  0.5032311263
##  [527,]  1.897145736  0.5354393211 -0.3064122557  0.0808995548
##  [528,] -1.217553028  0.8738065742  0.9731585577 -0.0477302733
##  [529,]  2.257587627 -1.9278276712  0.7539055291  0.1808899573
##  [530,] -1.500482593  0.7107920465  0.7067604040  0.1223484965
##  [531,] -0.218434082  1.3372554018  1.6942467846 -0.6347908280
##  [532,] -1.137368632 -0.2241664155 -1.1865139261 -0.1728918208
##  [533,]  3.132456689 -1.7873653189  0.8517569544  0.3649002674
##  [534,] -1.104004587 -0.2957801715 -1.3317085083 -0.2388046784
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##  [536,]  1.681474070  0.7260052685  0.1106418290 -0.0085398809
##  [537,] -0.265534027  0.4750241259  0.0054947675 -0.0487320175
##  [538,]  2.542959902  0.7175629035 -0.0814462170  0.2453008437
##  [539,]  1.573912241  0.6952563537  0.0706530929  0.0445414502
##  [540,]  3.329555277  0.6259625162 -0.4204697944  0.4595993658
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##  [544,] -1.323252191  0.3087103092 -0.1142455534  0.1195444407
##  [545,]  0.290128469  0.2914018738 -0.4624028324 -0.0889717641
##  [546,]  0.702260442  0.2992556891 -0.5284702887 -0.0890057069
##  [547,]  2.604507411  0.5641837788 -0.3930390173  0.2257021801
##  [548,]  2.025966641 -2.0434209587  0.5743165887  0.1511561407
##  [549,] -1.779151384  0.6049029925  0.5513350633  0.2859744556
##  [550,]  3.202674133  0.6450675148 -0.3568125881  0.4011198728
##  [551,]  3.362025767  0.5974089062 -0.4818847834  0.4209064894
##  [552,] -0.631283339  1.1475463826  1.3989098473 -0.3506745807
##  [553,] -1.443220224  0.6498755796  0.5768356227  0.0998656887
##  [554,]  0.252550667  0.2487772204 -0.5385754710 -0.0763696748
##  [555,]  0.961174074  0.7279292959  0.2585249782 -0.0941830860
##  [556,] -2.179910889  0.4149865507  0.2544871983  0.5096192052
##  [557,]  0.263281260  0.4357845112 -0.1754111369 -0.0619315910
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##  [559,] -1.694017720  0.0939951278 -0.4618592498  0.1716213223
##  [560,]  2.229702111  0.3975152459 -0.6437317244  0.1743794328
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##  [562,] -1.091137141 -0.0348263727 -0.8279982987 -0.0549800251
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##  [566,] -0.053270584 -0.2396443997 -1.4294351101 -0.2443047012
##  [567,]  1.827997486  0.9284739694  0.4771071436  0.0105042169
##  [568,]  0.913308574  0.1067684114 -0.9467170113 -0.0773334725
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##  [571,]  0.544662525 -1.7209054063  1.5027342681 -0.0969280354
##  [572,] -1.025617080  0.0755901997 -0.6255953298 -0.0308487862
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##  [588,]  2.864111448  0.7448577721 -0.0938772496  0.3557554938
##  [589,]  2.481246350  0.7971493956  0.0865134335  0.2368451888
##  [590,]  3.258766168  0.6318159490 -0.3941178360  0.4160761643
##  [591,] -0.739914165  0.9742884937  1.0785348542 -0.2033806311
##  [592,]  1.830504634  0.7213294677  0.0697458803  0.1004284995
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##  [594,] -1.755167541  0.1343920076 -0.3717068057  0.2141584709
##  [595,] -1.050844002  0.1244773357 -0.5254829700 -0.0099394510
##  [596,] -1.011641489  0.2576882687 -0.2739673362  0.0447623361
##  [597,] -1.307500380 -0.0385909949 -0.7931849131 -0.0280062689
##  [598,]  1.431220027  0.4614239571 -0.3579188942  0.0271557634
##  [599,] -0.310959295  1.2726927788  1.5835961660 -0.5069150169
##  [600,] -0.618218890  0.0522521294 -0.7501250237 -0.1054076855
##  [601,] -2.148285852  0.4281730361  0.2743243504  0.4951917175
##  [602,]  1.582172879  0.8367979518  0.3476514870 -0.0460946531
##  [603,]  1.697947741  0.2097854109 -0.9023847965  0.0190778336
##  [604,]  1.019238499 -0.0296192361 -1.2339546952 -0.0924963473
##  [605,]  2.277235189  0.8272401224  0.1891486453  0.0716913492
##  [606,]  0.541065110  0.3373005640 -0.4228132369 -0.0623694426
##  [607,]  0.088344264  0.8343382509  0.6413331292 -0.2046892586
##  [608,]  3.369738816  0.6124384117 -0.4548809847  0.4611739286
##  [609,]  2.861716043 -1.8287198570  0.8265609058  0.2630114464
##  [610,] -1.768292598  0.4149956299  0.1780079596  0.2822821784
##  [611,] -1.079432495  0.0479054609 -0.6697955195  0.0026014287
##  [612,] -0.302328719  1.2812815617  1.5996005170 -0.5502166827
##  [613,]  1.900456036 -2.2222074274  0.2514583020  0.0632679446
##  [614,]  0.724000688  0.6281323774  0.1102487099 -0.0925537933
##  [615,] -1.214170222  0.2991419913 -0.1529405607  0.0459653493
##  [616,] -1.885499395  0.4513362250  0.2709758768  0.3403470408
##  [617,]  2.900554160 -1.7819984831  0.9087960118  0.3304108207
##  [618,]  1.600556406  0.5787728150 -0.1616169279  0.0108979220
##  [619,] -0.945466070 -0.1315356478 -1.0436667744 -0.1573909752
##  [620,] -1.396189849 -2.0105968858  1.3120994846  0.2679512518
##  [621,]  2.039311129  0.6282299871 -0.1540661748  0.1265587455
##  [622,]  0.730658097  0.3292327082 -0.4759236650 -0.0679504223
##  [623,] -1.638517480  0.6723280793  0.6571204828  0.2031879319
##  [624,] -2.007603845  0.4942780724  0.3775823180  0.4094506014
##  [625,]  0.275487690 -0.0098006453 -1.0469171901 -0.1563791411
##  [626,] -0.070682533  0.0668872982 -0.8293596549 -0.1208291101
##  [627,]  2.883492436 -1.8076460256  0.8635513765  0.2585665528
##  [628,]  3.459590282 -1.7631369929  0.8336737304  0.4035000740
##  [629,]  1.603114530 -1.9556835434  0.8308775158  0.0805359074
##  [630,]  1.843248199 -2.2523018254  0.2048701277  0.0188314321
##  [631,]  0.124450836  0.6978439314  0.3659173970 -0.1367127807
##  [632,]  2.464690667  0.8114438502  0.1188022352  0.1862734946
##  [633,] -1.922404657  0.5298074069  0.4314852843  0.3492667075
##  [634,] -0.088247863  0.6174510895  0.2493897309 -0.0714485531
##  [635,]  2.681607106  0.5691796817 -0.4000571567  0.2988891466
##  [636,]  0.688451585  0.0479932180 -1.0164564209 -0.1122086828
##  [637,]  1.588390422  0.9008362273  0.4713860351 -0.0353028724
##  [638,]  2.358637105 -1.9751545714  0.6419766979  0.1546515517
##  [639,] -0.672257476 -0.1535209188 -1.1397794143 -0.1971437234
##  [640,] -0.101957181  1.2641317404  1.5268592720 -0.5677429452
##  [641,]  0.082126335  0.6485098439  0.2764906041 -0.0734315177
##  [642,] -1.028806835 -0.3454574155 -1.4425716491 -0.2911138745
##  [643,]  1.524682283 -1.9641862252  0.8314947243 -0.0016717424
##  [644,] -1.665774215  0.5480510351  0.4185980847  0.2480289767
##  [645,]  0.250225114 -2.4790261952  0.0803688095 -0.1702560569
##  [646,] -1.753514843  0.1333002000 -0.3741433582  0.2130088182
##  [647,]  0.733360701  0.6274734379  0.1069836842 -0.0865381702
##  [648,] -0.744266292 -2.7218045559 -0.1957872462 -0.2640351449
##  [649,] -0.105608419 -2.1664830361  0.7586122782 -0.0258688176
##  [650,] -1.269632476 -0.0956317315 -0.9115574955 -0.0572615668
##  [651,] -1.275885164 -0.1822321851 -1.0783070437 -0.1192408014
##  [652,] -1.218584626  0.8670253718  0.9604492332 -0.0639341788
##  [653,] -1.604284883  0.5814714629  0.4720886173  0.2337412753
##  [654,] -1.741017171 -1.8806422082  1.6309401747  0.4253599029
##  [655,] -0.509481193 -0.2610660198 -1.3797806589 -0.3104007714
##  [656,]  2.232972153  0.7543464360  0.0537344779  0.1496974528
##  [657,]  0.812972782  0.4706296311 -0.2165710240 -0.0297982459
##  [658,] -2.153321210  0.4287836828  0.2765692771  0.4925363620
##  [659,] -1.156729662  0.8912095581  0.9962492396 -0.0988715058
##  [660,] -2.018932848  0.4082192097  0.2114759164  0.4143276257
##  [661,] -1.445108950  0.2673032317 -0.1714902402  0.1369894646
##  [662,] -2.177431842  0.4133488394  0.2508323695  0.5078947262
##  [663,]  1.367403811  0.8592609603  0.4350925529 -0.0977733814
##  [664,] -0.579147415  1.1716749926  1.4366894521 -0.3935357362
##  [665,] -1.180627555 -0.1519698011 -1.0380846180 -0.1135962329
##  [666,] -1.313089719 -0.1124916092 -0.9358602014 -0.0606566696
##  [667,] -0.505065310  0.9654233043  1.0156716335 -0.2441607788
##  [668,] -1.643976554  0.1775991819 -0.3087408866  0.1922377337
##  [669,]  1.169102046  1.0337211608  0.8177081552 -0.2097959811
##  [670,] -0.701617260  1.1122044242  1.3436531849 -0.3478401265
##  [671,] -0.523295116  1.0619366735  1.2095349510 -0.3187492060
##  [672,] -1.268448023 -0.1871453191 -1.0892715301 -0.1244142384
##  [673,] -1.484346965  0.6446257899  0.5741714432  0.1246660278
##  [674,]  0.430135923 -1.5517783514  1.8572033882 -0.1538286827
##  [675,]  3.077450325 -1.8657046214  0.7097431120  0.3522378759
##  [676,] -0.691618253  1.0045053521  1.1287478095 -0.2355177432
##  [677,] -1.904570742  0.2671231959 -0.0850704256  0.3255529069
##  [678,] -0.619702252 -0.5127103294 -1.8463272616 -0.4815243489
##  [679,]  0.906755103  0.4494703300 -0.2770429071 -0.0025327888
##  [680,] -1.186639480 -0.2411897934 -1.2098808811 -0.1813220452
##  [681,]  1.390674210  0.7687721536  0.2516354903 -0.0054802042
##  [682,] -1.360962414 -0.0402878268 -0.7864271725 -0.0050465637
##  [683,]  1.516842469 -2.2339028159  0.3055597089  0.0077711199
##  [684,] -1.333729588 -0.1440189205 -0.9930277046 -0.0790029582
##  [685,] -1.684101533  0.0874442824 -0.4764785651  0.1647234063
##  [686,] -0.604423912  1.0442991624  1.1903543312 -0.2844312734
##  [687,] -1.418194032 -2.2835919274  0.7844313479  0.1888948386
##  [688,] -0.389125464  1.0112963117  1.0827018384 -0.2562266775
##  [689,]  1.183898927  0.5184632244 -0.1960822022 -0.0419403422
##  [690,] -2.170821051  0.4089816091  0.2410861593  0.5032961156
##  [691,]  0.074205758  0.2817288957 -0.4389502877 -0.0750416327
##  [692,] -0.834537702  1.0279002426  1.2025478794 -0.2274368430
##  [693,] -1.165519115 -0.1544648505 -1.0460843523 -0.1071318536
##  [694,] -1.342602374 -1.6983571966  1.9137392396  0.1825298350
##  [695,] -2.167515655  0.4067979940  0.2362130542  0.5009968103
##  [696,]  2.317047742  0.8528065875  0.2293566606  0.1616052911
##  [697,] -1.600302648  0.1147498462 -0.4394354471  0.1544698503
##  [698,]  1.321749700 -1.9467372493  0.9053559759  0.0144780602
##  [699,]  1.579207336  0.9953192003  0.6594364020 -0.1072367869
##  [700,]  1.210790517  0.9292660418  0.6036672542 -0.1343938736
##  [701,]  0.439287844  0.2662407856 -0.5409097678 -0.0960510437
##  [702,]  0.234990959  0.1578514027 -0.7126253697 -0.0875274048
##  [703,] -2.142619673  0.4210176552  0.2594642744  0.4835131502
##  [704,] -1.580489627  0.1388616329 -0.3962307580  0.1553381962
##  [705,] -0.082916959  0.1422332785 -0.6801035426 -0.0992017910
##  [706,]  0.997861324  0.9387218314  0.6659107778 -0.2140900186
##  [707,]  0.881378370 -2.4578046481 -0.0042496765 -0.1036552435
##  [708,]  0.006018899  0.2526633607 -0.4826995236 -0.0562528850
##  [709,]  0.069042241  0.1979371552 -0.6005777808 -0.1297783035
##  [710,] -2.185695331  0.4188078772  0.2630151322  0.5136429896
##  [711,] -0.274007379  0.0530352650 -0.8165792443 -0.1062673391
##  [712,] -0.370339377  1.1417296028  1.3362598121 -0.3636058185
##  [713,] -0.479711592 -0.0986783197 -1.0706053234 -0.1971095322
##  [714,]  0.015368512  1.3182264624  1.6107485063 -0.6297554425
##  [715,]  1.191172140  0.3964440509 -0.4377088509  0.0357245498
##  [716,]  1.230004587  1.0457646056  0.8290831544 -0.2033252725
##  [717,]  0.358314608  0.1934961176 -0.6666833808 -0.1168615425
##  [718,] -0.752482592  0.4477768830  0.0476788331 -0.0132972179
##  [719,]  2.179619376 -1.5672928219  1.4758666604  0.0994265889
##  [720,] -2.147970441  0.4249006690  0.2680167757  0.4880247561
##  [721,] -0.430995578  1.2162221541  1.4957581127 -0.4524645966
##  [722,] -0.934586341 -0.2562325912 -1.2882156388 -0.2223063940
##  [723,] -1.685949334  0.1662580307 -0.3228387904  0.2025472441
##  [724,]  0.894142747 -2.2652004934  0.3691505784 -0.0748946393
##  [725,] -1.680623950 -1.8839304789  1.6131892857  0.3966576355
##  [726,] -1.429088383  0.6339094568  0.5418793347  0.1447022075
##  [727,] -1.001909455 -0.1887858413 -1.1436797314 -0.1930882774
##  [728,]  0.679910616 -2.2865750335  0.3699273006 -0.0861411573
##  [729,]  1.543088643  0.8225504448  0.3273917753 -0.0400576963
##  [730,]  1.049696523  0.3921795666 -0.4169607059 -0.0177531697
##  [731,] -2.060438882  0.4634155536  0.3271122236  0.4364818479
##  [732,] -0.186597645  0.1852052282 -0.5759142990 -0.0849492207
##  [733,]  2.048719231  0.8955791003  0.3684967892  0.0433048950
##  [734,]  0.247858324  0.0713168642 -0.8833521309 -0.1340167184
##  [735,] -0.503075603  0.5360450217  0.1713463585 -0.0312524707
##  [736,]  0.907073946 -0.0762188964 -1.3017017490 -0.1487501722
##  [737,]  2.751283546  0.6855582725 -0.1856985633  0.2701728350
##  [738,]  0.922089225 -1.9760377019  0.9278518384 -0.0241116165
##  [739,]  2.745337154 -1.5754721202  1.3447902545  0.2559643959
##  [740,]  0.426971904  0.6175377408  0.1493480543 -0.1457867757
##  [741,] -1.140048192 -0.2311820295 -1.1993166068 -0.1909494481
##  [742,] -0.411986845 -0.2929758992 -1.4615487622 -0.3045337759
##  [743,] -0.302329766  1.1874193162  1.4132256794 -0.4145428661
##  [744,] -1.643972230  0.2081815628 -0.2489471107  0.1918850386
##  [745,]  3.428094186 -1.7563385144  0.8533959977  0.3936454341
##  [746,]  3.586307177 -1.7888998191  0.7573563345  0.4467513047
##  [747,] -0.944158278 -2.5491503654  0.1778102546 -0.1026244725
##  [748,] -0.878537118  1.0482427045  1.2522583356 -0.2863135505
##  [749,]  2.047305030  0.6652564041 -0.0836990854  0.1472279869
##  [750,] -0.518047766  0.4062174657 -0.0803960985  0.0108591034
##  [751,]  1.983285330  0.8529727801  0.2983366483  0.0335989639
##  [752,] -1.064460315 -0.0529255034 -0.8682349912 -0.0746159835
##  [753,] -0.963854549 -0.3374820463 -1.4398228535 -0.2906182365
##  [754,]  0.298740306 -2.5252009458 -0.0180899107 -0.2360314581
##  [755,] -0.345996608  1.2863486833  1.6186332586 -0.5737628477
##  [756,] -2.124387321  0.4422508166  0.2975190655  0.4765860679
##  [757,] -0.428057904 -0.0806525520 -1.0458382932 -0.1844946018
##  [758,]  2.472954157  0.8059848124  0.1066194725  0.1805252313
##  [759,] -2.165036608  0.4051602827  0.2325582254  0.4992723313
##  [760,] -0.029688187 -0.0029776516 -0.9728568960 -0.1766546209
##  [761,] -1.261342692 -0.1044042613 -0.9300642112 -0.0705020059
##  [762,]  1.569625251  0.9893120871  0.6500379624 -0.1285457153
##  [763,] -0.354307039  1.2731613139  1.5937914242 -0.5406315179
##  [764,] -1.594732604  0.3807631152  0.0784460847  0.2045097546
##  [765,] -0.287494106  0.0983480240 -0.7243230568 -0.1537444560
##  [766,] -1.801751759  0.5837119553  0.5142979145  0.2894924882
##  [767,]  0.501000967  0.4492214140 -0.1963638048 -0.0498388712
##  [768,] -0.752287842  0.1719052450 -0.4917170020 -0.0113644777
##  [769,] -1.880369068  0.5438112780  0.4506471001  0.3450452499
##  [770,] -0.256461578 -0.1550976312 -1.2246156388 -0.2156215353
##  [771,] -2.179910889  0.4149865507  0.2544871983  0.5096192052
##  [772,] -0.842846817 -0.2729751119 -1.3383481659 -0.2563660230
##  [773,]  0.653585961  0.1101683639 -0.8874586815 -0.1386034802
##  [774,]  3.236907612  0.6452928753 -0.3637288991  0.4290971829
##  [775,] -1.782117234  0.2195868746 -0.2005127124  0.2463115318
##  [776,] -1.101132029 -0.2462133028 -1.2363297703 -0.1938092032
##  [777,]  2.328374615  0.4429224276 -0.5738844398  0.1474032978
##  [778,] -1.723759091  0.1515283635 -0.3442913921  0.2085134569
##  [779,]  1.766798933  0.9217592201  0.4774355433 -0.0538223436
##  [780,] -1.626503007  0.2007147476 -0.2669338159  0.1889701559
##  [781,] -0.590954027  0.4217214443 -0.0351877482 -0.0124803322
##  [782,] -1.646089483  0.0623327085 -0.5325192736  0.1382813951
##  [783,]  0.311061105  1.0744357382  1.0691161408 -0.3179951819
##  [784,]  1.953432764 -2.1986226649  0.2880204495  0.0198482236
##  [785,]  1.157955043  1.0840108551  0.9189525063 -0.2441107897
##  [786,] -0.189852042  0.4632954375 -0.0316314372 -0.0843062233
##  [787,] -0.182131386  0.1380091505 -0.6683471199 -0.1186808761
##  [788,]  1.658299685  0.9647724373  0.5842163662 -0.1130433018
##  [789,]  0.844790437  0.8668738805  0.5543604557 -0.1513107229
##  [790,]  1.718097422  0.8396726159  0.3269232479 -0.0699231335
##  [791,] -1.984661766  0.5088832504  0.4019879391  0.3912734316
##  [792,]  0.017621739  0.4025784924 -0.1919301933 -0.0555195966
##  [793,] -1.577856377  0.2143321025 -0.2499276651  0.1891764723
##  [794,] -1.402019743 -0.0528256539 -0.8030033935  0.0032839973
##  [795,]  0.237963047  0.2194376944 -0.5928699404 -0.0848993476
##  [796,] -1.514484261  0.6123477494  0.5161315444  0.1666985309
##  [797,] -2.178258191  0.4138947432  0.2520506458  0.5084695526
##  [798,]  2.222486439  0.5919214960 -0.2626077093  0.1911957956
##  [799,]  2.097419072 -1.4979183454  1.6287497737  0.0513784138
##  [800,] -0.398429662 -0.2903840332 -1.4595156664 -0.2877795344
##  [801,] -0.995556301  0.8870605562  0.9567099166 -0.1183682895
##  [802,]  0.428675364  0.6190437099  0.1503752716 -0.0713042397
##  [803,] -0.867509713 -0.2200270682 -1.2306133233 -0.2257961353
##  [804,]  1.936363311  0.9094523048  0.4190608681 -0.0153836574
##  [805,] -0.919366763  0.2848725717 -0.2389742433  0.0410341867
##  [806,]  3.050031277  0.6372242254 -0.3404923268  0.3305675558
##  [807,]  1.213514445  0.1822957316 -0.8597238709 -0.0137200857
##  [808,] -1.359346405 -0.1270959033 -0.9552611401 -0.0611833419
##  [809,]  2.205777418  0.4658907919 -0.5052585676  0.1708220713
##  [810,]  2.847600120  0.6594518806 -0.2561475903  0.2882541588
##  [811,] -0.844588905  0.9173491609  0.9865066702 -0.1376680767
##  [812,] -0.992189274  0.7532071641  0.6933554800 -0.0706712578
##  [813,] -1.823130668 -1.9256843203  1.5582356836  0.4664494989
##  [814,]  0.015231636  0.0931668542 -0.7947268842 -0.1317119758
##  [815,] -1.034653249 -0.2924866378 -1.3388312167 -0.2453955409
##  [816,]  2.040415272  0.4083436645 -0.5839441393  0.1167645009
##  [817,]  0.422277993 -0.2392929241 -1.5219378020 -0.2801704929
##  [818,]  2.222438148  0.7828295928  0.1132656344  0.0664286098
##  [819,]  2.536566506  0.4998641083 -0.5070229305  0.3041523799
##  [820,]  0.764170916  0.4403408043 -0.2668126413  0.0017697411
##  [821,]  1.626584603  0.2826285120 -0.7466919579  0.0572906561
##  [822,] -1.287315744 -0.0051380982 -0.7322479331 -0.0056590006
##  [823,] -0.248379102  1.1818877416  1.3925796459 -0.4535007885
##  [824,] -0.301176802 -0.1003577733 -1.1091611305 -0.1970771927
##  [825,] -0.391736998 -2.7058426658 -0.2336039503 -0.2935048057
##  [826,] -1.690154773  0.5312509038  0.3903157091  0.2600750127
##  [827,]  1.888469307  0.6026665993 -0.1734007352  0.0869725543
##  [828,] -0.611852042  0.6155715943  0.3492908063 -0.0776036313
##  [829,]  1.991976537  0.2903418714 -0.8059552475  0.1588397365
##  [830,] -0.980644345  0.8632440423  0.9066167596 -0.0907064609
##  [831,]  1.775803697  0.9037369117  0.4396586320 -0.0177617544
##  [832,]  0.718857287  0.2497411986 -0.6294059092 -0.0485606073
##  [833,] -0.833687139 -2.5745070275  0.1072323590 -0.1411876764
##  [834,]  2.260440877 -1.8017775193  0.9995667308  0.1901909750
##  [835,]  1.337255339  0.8023705821  0.3286442865 -0.0418567368
##  [836,] -1.774999915  0.1474936983 -0.3424681751  0.2279543028
##  [837,]  0.399803256  0.3223881132 -0.4238938582 -0.0701186336
##  [838,] -0.936380515  0.9873496770  1.1426417065 -0.1919920463
##  [839,]  2.179479803 -1.9496163644  0.7276398861  0.1385179118
##  [840,]  3.007587734  0.6876430897 -0.2337647485  0.3411367595
##  [841,] -1.870374160  0.5632092709  0.4869701558  0.3273478706
##  [842,] -1.620610449  0.4614663205  0.2408452781  0.2273380369
##  [843,] -1.023022392 -0.3492787419 -1.4510995830 -0.2951376588
##  [844,] -1.770685763  0.5954920279  0.5315732202  0.2714274578
##  [845,]  1.904973786  0.7327121171  0.0784285267  0.0465846164
##  [846,] -1.591395342  0.4257519598  0.1649955284  0.2394975009
##  [847,]  2.562990804  0.7968981964  0.0699720805  0.2321600030
##  [848,]  2.448714628  0.8098348109  0.1191622895  0.1698070877
##  [849,]  3.439316005  0.6057491448 -0.4825666862  0.5018295425
##  [850,]  1.325410808  0.5247232064 -0.2130330274  0.0160912213
##  [851,] -2.064585965  0.3750610394  0.1550872316  0.4419157522
##  [852,] -1.270831634 -0.0081009142 -0.7414348250  0.0008484596
##  [853,] -0.237987106  1.3098001360  1.6431319218 -0.5733307816
##  [854,]  2.361032923  0.5665144575 -0.3407851422  0.2447449196
##  [855,]  2.329768106  0.8426739392  0.2073056695  0.1488355701
##  [856,] -1.669227253  0.0776180144 -0.4984075380  0.1543765324
##  [857,]  2.122174298  0.7178928761  0.0050411744  0.1175462271
##  [858,]  1.525047644  1.0101725220  0.6993812932 -0.1170107675
##  [859,] -1.485682414  0.7488498410  0.7791125252  0.0811161399
##  [860,]  2.126009898  0.6413522184 -0.1446907270  0.0864714305
##  [861,] -0.215244250 -2.2679155163  0.5828072098 -0.0650239194
##  [862,] -0.830151303 -0.3721395774 -1.5331213440 -0.3316313062
##  [863,]  0.114865431 -0.0540680727 -1.1012975681 -0.1765223549
##  [864,] -1.039427478 -0.2001567792 -1.1587903641 -0.1792721530
##  [865,]  0.189592082  1.0690363805  1.0834071178 -0.3579944511
##  [866,] -2.054663910  0.4622466658  0.3236441072  0.4384648127
##  [867,]  1.671397530  0.6340903128 -0.0683788776  0.0537645154
##  [868,] -1.999511429  0.3731021012  0.1388666250  0.4199836450
##  [869,]  2.731246468  0.7385640913 -0.0773672992  0.2348840688
##  [870,]  1.969118266  0.4985090097 -0.3937557934  0.1246071431
##  [871,] -0.337513664  1.2842380936  1.6127883704 -0.5717425031
##  [872,]  0.535123171  0.9429095692  0.7657989874 -0.2273546168
##  [873,]  1.452114263  0.2842226603 -0.7091709903  0.0603258912
##  [874,] -1.865223934  0.2807446057 -0.0660609278  0.3183069556
##  [875,] -0.025739745 -0.2781888926 -1.5088411669 -0.3096148870
##  [876,]  0.496305932  0.7291602711  0.3532321710 -0.1158610197
##  [877,]  1.054255883  0.8316512012  0.4422478896 -0.0631184354
##  [878,] -0.411139432  0.5047346511  0.0933930243 -0.0981866131
##  [879,] -0.214392747 -0.4181255755 -1.7425906049 -0.4297736850
##  [880,] -1.238466984 -1.6361870113  2.0158575778  0.1282453932
##  [881,] -0.888712772 -0.2038031161 -1.1951268988 -0.2060203744
##  [882,]  2.972601376  0.5529783076 -0.4904362648  0.3562221762
##  [883,] -0.319042954  0.9175777506  0.8845197895 -0.2033995207
##  [884,] -2.177431842  0.4133488394  0.2508323695  0.5078947262
##  [885,] -0.584445282 -2.5839786934  0.0401241403 -0.1717951582
##  [886,]  0.945607898 -2.5262916568 -0.1486264625 -0.2074152378
##  [887,]  0.730940347  0.2196145047 -0.6894456584 -0.1071777225
##  [888,]  2.332972033  0.5665668901 -0.3331847860  0.1526488525
##  [889,]  0.440689837  0.1474303782 -0.7736790271 -0.0855220156
##  [890,]  1.744270485  0.3174712920 -0.7010693455  0.0216148380
##  [891,]  0.513182458 -2.1509374044  0.6673023988 -0.0517576999
##  [892,] -2.102234090  0.3636715954  0.1399692287  0.4555855301
##  [893,]  1.657301836  0.7272110534  0.1181281041 -0.0251997308
##  [894,]  0.457673081  0.0741500082 -0.9185364846 -0.1683565802
##  [895,]  3.373432813  0.5830455387 -0.5132001642  0.4671910550
##  [896,]  2.032276355  0.3639354795 -0.6698348771  0.1489419672
##  [897,] -0.328255504 -0.2670068359 -1.4270396475 -0.3178720101
##  [898,]  1.561043715  0.4167998751 -0.4723473183  0.0998332100
##  [899,] -2.161418582  0.4322760103  0.2849661847  0.4939584313
##  [900,] -0.463411359 -0.3063249432 -1.4774471902 -0.3063604629
##  [901,] -0.150461184 -0.1279512821 -1.1926402596 -0.2084233246
##  [902,]  2.213129897  0.4170516907 -0.6029226110  0.2053816336
##  [903,]  1.876172251  0.7937595000  0.2039745280  0.0224979983
##  [904,] -0.187329921 -2.7230819049 -0.3073816726 -0.3079960149
##  [905,] -1.456756243  0.0615890460 -0.5701289830  0.0793984076
##  [906,] -0.681542804  0.1933733068 -0.4630039086 -0.0453278472
##  [907,] -1.976012455  0.5087866646  0.3999477410  0.3979939668
##  [908,]  3.200311644  0.6227745042 -0.4002938024  0.4183765271
##  [909,] -0.680013377 -2.4169255009  0.3836127106 -0.0787852819
##  [910,] -0.130524791 -2.5063001911  0.1026708573 -0.1890784008
##  [911,]  3.100243750  0.6862269724 -0.2563477811  0.4122658031
##  [912,] -1.855501748  0.5620075408  0.4814872277  0.3365554530
##  [913,]  0.037563168  1.3240372908  1.6170661759 -0.5987722294
##  [914,] -1.051463681 -2.5632134146  0.1710627174 -0.0812036198
##  [915,] -0.066445476 -2.2419160623  0.6048905810 -0.0957891988
##  [916,]  1.562581534  1.0055597726  0.6825312407 -0.0973557726
##  [917,]  0.005022434  0.1528149650 -0.6773176279 -0.0743532975
##  [918,]  0.291831878 -0.1696096431 -1.3610707347 -0.2268250721
##  [919,] -0.337506198  1.1724007756  1.3906571657 -0.4071188898
##  [920,] -1.852374807  0.5571447559  0.4715436592  0.3280380091
##  [921,] -0.598952410  0.0437140690 -0.7705400923 -0.1093096137
##  [922,]  1.581207693  0.7362905590  0.1517700662 -0.0656642316
##  [923,]  0.064352107 -2.3162567041  0.4335883448 -0.0897120376
##  [924,]  0.131277009  0.2852660077 -0.4429733910 -0.0909327836
##  [925,] -0.872901977 -2.5967344690  0.0717841867 -0.1533498350
##  [926,] -0.642461298 -0.0668255623 -0.9764221225 -0.1857608718
##  [927,]  2.737072439  0.6283443228 -0.2947048805  0.2684416459
##  [928,]  0.289252548  0.1543543944 -0.7294585240 -0.1216225295
##  [929,] -0.597043994  0.0479662073 -0.7628414505 -0.0981368143
##  [930,]  0.295272782  0.2608884059 -0.5231700293 -0.0843319404
##  [931,] -0.201092547  1.3683767765  1.7528268987 -0.6897123799
##  [932,] -0.720861909 -2.6347547266 -0.0318613290 -0.1872757597
##  [933,] -1.586777085  0.4204378584  0.1538713537  0.2311532238
##  [934,] -0.757831523 -2.6221003553  0.0002017514 -0.1882438176
##  [935,] -0.985695182 -0.1532439167 -1.0779073164 -0.1691896969
##  [936,]  2.761538392  0.5467136091 -0.4600486051  0.3120785224
##  [937,] -1.774157026  0.6036230675  0.5478227255  0.2870793416
##  [938,] -1.489469632  0.7130220136  0.7086493709  0.1362408515
##  [939,] -1.635417436  0.4686483749  0.2577177091  0.2317432045
##  [940,] -0.109841490  0.1290519626 -0.7009395019 -0.0809912570
##  [941,]  1.594222937  1.0107239990  0.6855887980 -0.0602593721
##  [942,]  2.020968881  0.3909184929 -0.6144771740  0.1313520674
##  [943,] -1.192758099 -0.1490511654 -1.0299161874 -0.1167109041
##  [944,] -2.085159026  0.4485574577  0.3026058761  0.4526589492
##  [945,]  0.759792476 -2.2518652834  0.4219295832 -0.0827485991
##  [946,]  1.097492431 -2.2779460145  0.3041685749 -0.0800448092
##  [947,] -1.182006938  0.8669207342  0.9524006320 -0.0348243195
##  [948,] -1.489737082 -2.2367120583  0.8891760831  0.2377932994
##  [949,] -0.966949186 -0.0860966589 -0.9509328610 -0.1412964984
##  [950,] -0.773495578  0.3443545937 -0.1509377449  0.0141399834
##  [951,] -0.956566434  0.2017682424 -0.3938953196  0.0318539189
##  [952,]  0.138955666 -0.0566124143 -1.1113186655 -0.1629634439
##  [953,] -1.770041822  0.1442182756 -0.3497778328  0.2245053448
##  [954,]  0.023024650  1.3093005709  1.5906064351 -0.5741509567
##  [955,] -1.448095094  0.0581769120 -0.5784939530  0.0786105063
##  [956,] -0.048176408  0.1219639271 -0.7262088718 -0.1172889656
##  [957,]  0.382809605  0.1910093508 -0.6766815486 -0.1028473314
##  [958,] -1.582744705 -2.0021601059  1.3637825614  0.3465073791
##  [959,] -1.705751462  0.6240949082  0.5751382004  0.2489800484
##  [960,] -0.959129446 -2.3167671729  0.6315356869  0.0637824387
##  [961,]  1.347199679 -1.7037073726  1.3766247038 -0.0413473129
##  [962,] -1.753514843  0.1333002000 -0.3741433582  0.2130088182
##  [963,] -0.238289481 -2.7370282588 -0.3245188498 -0.3108040463
##  [964,] -2.027096882  0.5014570136  0.3954543752  0.4100889834
##  [965,] -2.107152008  0.4314334969  0.2731936668  0.4658863165
##  [966,]  1.946124762  0.8941914159  0.3863871768  0.0275454990
##  [967,] -0.876649752 -0.4000471895 -1.5778377486 -0.3625169388
##  [968,] -1.012279856 -0.3563754911 -1.4669371745 -0.3026104011
##  [969,]  1.476775848  0.4027597603 -0.4825157740  0.0700885545
##  [970,]  1.098309169  0.7482257604  0.2707576173 -0.0775367534
##  [971,] -0.401736841 -1.4954627179  2.1312659205 -0.1359564325
##  [972,]  1.358726322  0.7169966215  0.1568054559 -0.0091105262
##  [973,]  3.017669951  0.6392555055 -0.3296746939  0.3092092010
##  [974,] -1.353561963 -0.1309172298 -0.9637890741 -0.0652071262
##  [975,] -0.802218360 -0.0299662256 -0.8748132303 -0.0909577743
##  [976,]  2.652503815 -1.8666299566  0.7947297018  0.2182984851
##  [977,] -0.288206298  0.5369433560  0.1313879884 -0.0659240909
##  [978,] -1.640015899  0.6747687248  0.6620959522  0.2075198270
##  [979,] -1.068402284  0.9417796786  1.0781613633 -0.1224409210
##  [980,] -0.320950109  0.6639010798  0.3864184318 -0.0831255163
##  [981,] -1.077561421 -0.3132490924 -1.3706933490 -0.2571991210
##  [982,] -0.020574489  1.3350075411  1.6504602748 -0.6205426048
##  [983,]  0.538608819 -2.1313347287  0.7007043727 -0.0566099542
##  [984,] -1.390649128  0.3129926870 -0.0930961556  0.1448815820
##  [985,] -2.182389936  0.4166242621  0.2581420271  0.5113436842
##  [986,] -1.450317558  0.7718565412  0.8168727751  0.0919563219
##  [987,] -1.242685039  0.8608802324  0.9524241437 -0.0275034102
##  [988,]  1.352736248  0.6303702934 -0.0115286752 -0.0012366713
##  [989,] -0.403532037  1.1416522918  1.3432350849 -0.3904123568
##  [990,] -1.459926614  0.6427918515  0.5654341352  0.1401006226
##  [991,] -1.814797974  0.4688174039  0.2920959682  0.2973085046
##  [992,] -1.833118709  0.5752063061  0.5033310024  0.3147407406
##  [993,]  0.494162723  0.2455181767 -0.5921999404 -0.0990117343
##  [994,]  0.077984841  0.3799827611 -0.2479698150 -0.0583242240
##  [995,] -0.544750016 -2.7384125860 -0.2673118528 -0.2810191025
##  [996,] -0.124208071  1.3607365835  1.7217598857 -0.6453501650
##  [997,] -1.306221341 -0.1201394316 -0.9519172619 -0.0724872845
##  [998,] -0.632786400 -0.3099770403 -1.4510233731 -0.3111329011
##  [999,]  0.098675866 -2.1823496189  0.6889572366 -0.1070471347
# Identifying the scores by their survival status
teletype_pca <- cbind(data.frame(Churn),telecom_pca$x)
teletype_pca
##     Churn          PC1           PC2           PC3           PC4
## 1      No -2.015467453  0.3063516984  0.0120502201  0.3952287653
## 2      No -0.286167867  0.5013439720  0.0615892254 -0.0753083935
## 3     Yes -1.580345244  0.0591421382 -0.5512321189  0.1140939064
## 4      No -0.287614123  0.7983943370  0.6445959152 -0.1696250516
## 5     Yes -1.294160708 -0.1237314581 -0.9613547414 -0.0709556042
## 6     Yes -0.494044929 -0.3379468993 -1.5326506543 -0.3329395336
## 7      No -0.020111087  0.0003749667 -0.9685190929 -0.1613687025
## 8      No -1.733455753  0.4319562059  0.2043525014  0.2789892675
## 9     Yes  0.688536938 -0.0510378498 -1.2097481522 -0.1275878542
## 10     No  0.800699638  0.9284002528  0.6841006823 -0.1865781716
## 11     No -1.254566657  0.2600970846 -0.2216823424  0.0644229830
## 12     No -1.764971394  0.6268866250  0.5916904672  0.2774977466
## 13     No  2.061385552  0.4838318990 -0.4400631575  0.0956542225
## 14    Yes  1.724378831  0.3072806955 -0.7177116306  0.0522494039
## 15     No  0.527494462 -0.1112877649 -1.2945144595 -0.1843081668
## 16     No  3.161504599  0.5720136417 -0.4917171390  0.4115436863
## 17     No -0.716173101  1.0901673293  1.3032764892 -0.3397861962
## 18     No  2.952410314  0.6478858084 -0.2992142283  0.2764189167
## 19    Yes -1.254731788  0.1623572800 -0.4124580865  0.0517707540
## 20     No -0.052469384 -0.0261847489 -1.0136995538 -0.1778530396
## 21    Yes -1.611728253 -2.1930906514  0.9970540300  0.3085286329
## 22     No -1.878281489  0.5620845058  0.4865222098  0.3184532575
## 23    Yes -2.175779144  0.4122570318  0.2483958170  0.5067450736
## 24     No  0.775447113  0.8376438460  0.5105457067 -0.1338228327
## 25     No  0.410974980  0.7056174597  0.3236927933 -0.0983047154
## 26     No -0.507827005  0.4543022412  0.0135374770 -0.0810125188
## 27    Yes  1.525172980  0.3179618635 -0.6575552351  0.0560433902
## 28    Yes -2.009683010  0.3025303719  0.0035222862  0.3912049809
## 29     No  2.415256278  0.7991045643  0.1058810951  0.1186320774
## 30    Yes -0.777763717  0.1696083634 -0.4906300199 -0.0370124895
## 31     No  2.848230035 -1.6564358066  1.1668468777  0.2246353601
## 32     No -0.641013427 -2.7867310927 -0.3417486462 -0.3284125213
## 33     No -0.300560723  0.3117621795 -0.3071772993 -0.0288213652
## 34     No -2.174952795  0.4117111280  0.2471775407  0.5061702472
## 35     No -1.519177173 -2.2542318748  0.8606070875  0.2441480838
## 36     No  2.827024440  0.7296306943 -0.1149545366  0.2914726586
## 37    Yes -1.194294975 -0.0682028508 -0.8724635335 -0.0740242687
## 38     No  0.756572527  0.5250342636 -0.0992482896 -0.0213891894
## 39    Yes  0.995843188  0.0282164677 -1.1156929653 -0.1195278411
## 40    Yes -0.372576730 -0.2687303412 -1.4222942619 -0.2876389053
## 41     No -1.361697679  0.2221115384 -0.2755626470  0.1014410539
## 42     No  1.595061949  0.9430453465  0.5533983805 -0.0736439939
## 43     No -1.686527850  0.6235121074  0.5699017654  0.2630821071
## 44     No  1.605413825  0.7377433815  0.1493460653 -0.0429488503
## 45     No -0.714410979 -0.0113787300 -0.8552542721 -0.1177632548
## 46     No  1.086026186  0.4712426940 -0.2680799863 -0.0881353262
## 47     No -1.658263057  0.1090959181 -0.4392579796  0.1648477748
## 48    Yes -1.134762350 -0.2330839393 -1.2040775207 -0.1910210350
## 49     No  1.167167537  0.5738663650 -0.0853678670  0.0005600547
## 50     No  1.311538924  0.9603726853  0.6458001905 -0.1921306285
## 51     No  1.264868979 -2.0625593971  0.6907915360 -0.0149786634
## 52    Yes -0.168370241 -0.2188635628 -1.3651104889 -0.2895317085
## 53     No -0.085154857 -2.1475877081  0.7917325457 -0.0363147592
## 54    Yes -0.614912060 -2.5298658743  0.1513254615 -0.1432407568
## 55     No  1.580551201 -1.6543390313  1.4266039081 -0.0209865789
## 56    Yes  0.176758767 -2.5201212919  0.0148139888 -0.1829799378
## 57     No  2.346069747  0.5803719891 -0.3096712143  0.1944602172
## 58     No  3.020282165 -1.8392739689  0.7738886278  0.2966004227
## 59     No -1.093507929  0.8111109188  0.8255104785 -0.0206660269
## 60     No  3.124480162  0.6710979411 -0.2903972792  0.3974064804
## 61     No  1.531689184  0.3036294823 -0.6862831312  0.0287731236
## 62     No  1.870638938  0.6140627227 -0.1478439577  0.0985073036
## 63     No  0.648254123  1.1866591365  1.2240615826 -0.4203028134
## 64     No -0.961557792  0.2894863205 -0.2211229268  0.0176449277
## 65    Yes -0.545892972 -0.2663085838 -1.3834428268 -0.2818011253
## 66     No -1.169962034 -0.1577506121 -1.0513963954 -0.1181469042
## 67     No  0.875427786  0.4968895086 -0.1769417601 -0.0595475609
## 68     No  0.182493361  0.2447198211 -0.5327578437 -0.0720772747
## 69     No -0.796456606  1.0666790373  1.2727579581 -0.3180565883
## 70     No -0.750675757 -0.0930231842 -1.0075922102 -0.1228832013
## 71     No -1.698149465  0.0967246467 -0.4557678685  0.1744954540
## 72     No -0.700659398  1.0956912830  1.3104807748 -0.3148137478
## 73     No  3.032428488 -1.8980463204  0.6562547371  0.3124827647
## 74     No -0.313836135  1.1931437520  1.4280892831 -0.4804957131
## 75     No -1.364614999 -0.0421342756 -0.7891642665 -0.0121639001
## 76     No  2.554954116 -2.0261799036  0.5025524213  0.1964623697
## 77     No  0.197136523  0.6995581852  0.3535888524 -0.0745083433
## 78     No -1.322542296  0.1413066356 -0.4410049403  0.0890350495
## 79     No  0.217664019 -2.1274182062  0.7726062771 -0.0961275654
## 80     No -0.734366957  0.9524571386  1.0342366316 -0.1787310509
## 81    Yes -1.197382016 -0.2340930443 -1.1940432895 -0.1738493029
## 82     No -1.296764834  0.2274303565 -0.2778753067  0.0958974213
## 83    Yes -1.008206279 -0.0953456690 -0.9611949560 -0.1256688903
## 84     No  1.361647046  0.1888972503 -0.8759652645 -0.0193031968
## 85     No -0.806959336  1.0558336138  1.2528522851 -0.2813738779
## 86     No -0.448546799 -0.3174794868 -1.5019068907 -0.3197269722
## 87     No -0.084717836  0.4703519543 -0.0392572419 -0.0536551817
## 88     No -0.797431545  1.0412029346  1.2214304455 -0.2372032057
## 89     No -0.891905672  1.0183499064  1.1951683772 -0.2254186136
## 90     No -1.031259395  0.6564413875  0.5098277540  0.0270728460
## 91     No  0.227101041  0.2038970410 -0.6216515858 -0.0591512269
## 92     No -1.032457656 -2.5757692015  0.1430423631 -0.0944246254
## 93     No  1.987686410  0.7651075091  0.1239313568  0.1167016622
## 94     No  2.806811496  0.5133466217 -0.5333892179  0.2727432484
## 95     No  2.903210552  0.7271987352 -0.1359404036  0.3470841182
## 96    Yes -0.708173758 -0.0563325608 -0.9437915035 -0.1449897800
## 97     No  1.543929464  0.9763055519  0.6292716107 -0.1089530202
## 98    Yes -2.042972026  0.4566118480  0.3103904728  0.4350686525
## 99     No -0.686131807  1.0897963793  1.2961226931 -0.3165244945
## 100   Yes  0.606006347 -2.4340735414  0.0971351316 -0.1313806771
## 101    No -2.174952795  0.4117111280  0.2471775407  0.5061702472
## 102    No -2.187348029  0.4198996847  0.2654516848  0.5147926422
## 103    No  0.918938002  0.2052854759 -0.7556317176 -0.0585346918
## 104    No  0.828260114 -1.3164589611  2.2411930707 -0.2766375917
## 105   Yes  3.004049207  0.5833891941 -0.4377168502  0.3807084725
## 106    No -1.994145410  0.4204330920  0.2309257221  0.3922088180
## 107    No  2.910881473  0.6851658542 -0.2177366027  0.2579300175
## 108    No -1.044980444  0.7303122424  0.6580689327 -0.0255384601
## 109    No  1.113535949  0.2883479476 -0.6316082014 -0.0625671835
## 110    No -0.182569918  1.3696846049  1.7513460190 -0.6718857738
## 111   Yes  1.806754913  0.4673260818 -0.4213335735  0.0630347745
## 112    No  0.473311559  0.7644325971  0.4269041449 -0.1240317493
## 113    No  1.079176733  0.3192866846 -0.5652398537 -0.0199814513
## 114   Yes  0.624327885 -2.0273332320  0.8865403656 -0.0308186348
## 115    No  0.802448837  0.9679188640  0.7620389149 -0.2349692600
## 116    No -0.932457938 -0.3170301421 -1.4060826680 -0.2887548140
## 117    No -0.881816122  0.7789851697  0.7217833082 -0.0630673719
## 118   Yes -0.368163059 -0.3092994349 -1.5020791769 -0.3063862092
## 119    No -1.021001971  0.9439411638  1.0735904064 -0.1492104927
## 120    No  0.088899116  0.1143871675 -0.7671133245 -0.1638923674
## 121    No  1.959011199  0.4578647766 -0.4705680350  0.0940391395
## 122    No -2.026197593  0.4729935049  0.3395070540  0.4159711657
## 123   Yes -1.188782751 -0.1484856985 -1.0296909860 -0.1122392064
## 124    No -1.447591995  0.1665799333 -0.3674576470  0.1157125107
## 125    No -2.083725783  0.4441172020  0.2938314490  0.4437406886
## 126    No  0.539725647  0.1848646509 -0.7205916833 -0.0605840051
## 127   Yes  0.209918439 -2.2003618683  0.6307395561 -0.0586370421
## 128    No -0.010898566  1.3390376628  1.6560687648 -0.6036411741
## 129    No -2.182389936  0.4166242621  0.2581420271  0.5113436842
## 130    No  1.396133635 -1.3335566399  2.0941270073 -0.2082934779
## 131    No -0.488380801 -0.1085994906 -1.0891420399 -0.1568600231
## 132   Yes -0.576201423  0.3540315690 -0.1703852335 -0.0147272045
## 133    No  0.757771042  1.0433573449  0.9199122068 -0.3088633185
## 134   Yes -1.922916373  0.2452104750 -0.1243967224  0.3308482161
## 135   Yes -1.742382162  0.1621482838 -0.3200446092  0.2176521793
## 136    No -0.791376856  0.9282986842  0.9974460071 -0.1398480704
## 137    No -0.275699196  0.1604626277 -0.6069323676 -0.0731386512
## 138    No -0.376504769  1.2566716754  1.5656327046 -0.5261301134
## 139    No -0.576670736  1.1707003910  1.4342995777 -0.3937585278
## 140   Yes -1.102697315 -2.5293673802  0.2465958462 -0.0455643873
## 141    No  2.637556123 -1.5669191859  1.3842277020  0.1888827841
## 142   Yes -1.031083507 -0.0361726080 -0.8419731597 -0.0795512270
## 143    No  2.224966267  0.5258663614 -0.3905755385  0.1131078737
## 144    No  1.824074123  0.7191511070  0.0684508781  0.0206287085
## 145    No  0.223919674 -1.0690561234  2.8500292312 -0.5490385180
## 146    No  2.412380218  0.6164685312 -0.2521123012  0.1901086577
## 147    No -2.127246954  0.4451612849  0.3036825113  0.4808911428
## 148   Yes -1.754341192  0.1338461038 -0.3729250820  0.2135836445
## 149    No -0.242980107  0.3699008128 -0.2042353704 -0.0598981756
## 150    No -0.751647226  0.0909294433 -0.6492204286 -0.0550592777
## 151    No -1.073099568 -0.0076498994 -0.7785687452 -0.0485870504
## 152   Yes -0.640030879 -0.3063633944 -1.4425781495 -0.3087514494
## 153    No  3.111701929  0.6419525586 -0.3461887078  0.4604697940
## 154    No  1.786414072  0.6712071826 -0.0178471279  0.0211034744
## 155    No -2.042218618  0.4839835491  0.3639012414  0.4280368175
## 156    No -0.565777248 -0.0432490520 -0.9464418700 -0.1404773148
## 157    No -0.137336369  0.0493816447 -0.8499160814 -0.1442996565
## 158    No -1.581914961  0.6931113543  0.6875625870  0.1563249540
## 159    No -0.827824399  0.1591071012 -0.5013908336 -0.0312876590
## 160    No -1.813761641  0.4742723869  0.3022753840  0.3105090355
## 161    No -1.105125107  0.2010771358 -0.3662922662  0.0504969156
## 162   Yes -0.277685139  0.0339356276 -0.8522100655 -0.1525261096
## 163    No -1.315154533 -0.1134487617 -0.9372422605 -0.0644836397
## 164    No  1.019911639  0.6398949025  0.0736162178 -0.0375695116
## 165    No -1.878916383  0.5420275733  0.4469341284  0.3421662599
## 166    No -0.242720302  1.3264397073  1.6773555496 -0.6090995206
## 167   Yes -1.210277456 -0.0957504472 -0.9230417556 -0.0796099086
## 168    No  2.362522478  0.8075262451  0.1332558771  0.0954185136
## 169   Yes  0.533272788 -1.4299135605  2.0763220454 -0.2129601398
## 170    No -1.742987721  0.6107737100  0.5562482640  0.2586000645
## 171    No  0.839076685  0.3833241167 -0.3916082964 -0.0674157512
## 172   Yes -0.720591805 -0.4893079825 -1.7815320167 -0.4397049858
## 173    No -0.540357577 -0.0535656476 -0.9715687177 -0.1434751867
## 174   Yes  1.661339506  0.4531497085 -0.4201193144  0.0536221318
## 175    No -1.279821564  0.8242893656  0.8876622997 -0.0008657922
## 176    No -1.130555556  0.8091583715  0.8297371924 -0.0548175517
## 177   Yes -0.408013662 -2.3527082303  0.4550920136 -0.0634476390
## 178   Yes -0.743385170 -2.5017623018  0.2310042629 -0.1128923886
## 179    No -0.028474511 -0.2818951271 -1.5153215325 -0.3202128601
## 180    No -0.446593399  1.2140034675  1.4948745044 -0.4700099121
## 181   Yes -2.013814755  0.3052598908  0.0096136676  0.3940791126
## 182    No -1.760125634  0.1376674302 -0.3643971480  0.2176074288
## 183   Yes -0.785685539 -0.1784065725 -1.1658501246 -0.2051752464
## 184    No  0.143094098  0.3168652298 -0.3837755166 -0.0795021588
## 185   Yes -0.627242566 -0.0394498337 -0.9274866262 -0.1114766533
## 186   Yes -2.098928694  0.3614879802  0.1350961236  0.4532862247
## 187    No -0.938926300  0.3459076749 -0.1154348647  0.0243347932
## 188    No -1.945864424  0.3276573170  0.0406986193  0.3599807990
## 189    No -1.845639560  0.5780694231  0.5114773223  0.3111870300
## 190    No -0.013645536  0.6008614722  0.2017472848 -0.0492099881
## 191    No  0.532751459  0.5036226535 -0.0964845987 -0.0404131894
## 192   Yes -0.763753011 -0.2802378127 -1.3676905617 -0.2790763147
## 193    No -0.241701043  1.3285750295  1.6812085557 -0.6034399477
## 194    No  3.239883891  0.6583217136 -0.3395236129  0.4610277318
## 195    No -0.529586745  1.2000814152  1.4831787898 -0.4287632277
## 196    No  0.041504261 -0.1084171375 -1.1921482007 -0.2192149388
## 197    No -1.423797011  0.6818932760  0.6351992915  0.1183477642
## 198    No  2.505245073  0.4103612382 -0.6739275213  0.2154787463
## 199    No  3.255949403  0.6267711577 -0.4031330238  0.4023772523
## 200    No -2.165862957  0.4057061865  0.2337765017  0.4998471576
## 201    No  0.513172914 -0.0468538068 -1.1656179976 -0.1890981702
## 202    No -0.591288638 -0.0355992888 -0.9263805723 -0.1436000171
## 203    No  2.940458725  0.6614450421 -0.2707942440  0.2975751530
## 204    No -0.665132866 -0.0322339955 -0.9055964102 -0.1255151563
## 205    No  0.444015173  0.5408222174 -0.0050303649 -0.0969602015
## 206    No  0.294475844  0.2693998505 -0.5067690248 -0.0656718236
## 207    No  1.216941856  1.0904109992  0.9184988127 -0.1822721193
## 208   Yes -1.188292177 -0.2400979858 -1.2074443285 -0.1801723925
## 209   Yes  0.191402077 -0.2297993808 -1.4572500566 -0.3044790441
## 210    No  2.513449429  0.5763791191 -0.3517235008  0.2499979911
## 211   Yes -1.714650062  0.1441992588 -0.3602215210  0.1992032533
## 212    No -2.091491554  0.3565748462  0.1241316372  0.4481127878
## 213    No -0.496532742  1.2175150698  1.5122868829 -0.5021149164
## 214    No -1.390183335  0.7878346061  0.8373942404  0.0370312003
## 215    No  0.214739477 -2.3531851542  0.3323793816 -0.1224883096
## 216    No  0.714439146  0.8348736551  0.5168759742 -0.1193512227
## 217    No  0.750808255  1.1594496565  1.1501706444 -0.3997181818
## 218    No  0.986205791  0.9862221755  0.7604665072 -0.1854365658
## 219    No  1.855475220  0.7342960777  0.0920706096  0.0104623719
## 220    No -0.869756792 -0.1306549715 -1.0567547514 -0.1643518188
## 221   Yes -1.223800243 -0.0877222775 -0.9048314868 -0.0722558497
## 222    No  0.018466833  1.3179405019  1.6080594762 -0.5582169394
## 223    No -2.174952795  0.4117111280  0.2471775407  0.5061702472
## 224   Yes -1.575912620  0.1288975389 -0.4162128889  0.1364170651
## 225    No -1.880644639  0.5677193812  0.4977741351  0.3293342068
## 226    No -0.790721995  0.4203173894  0.0005657508  0.0331607291
## 227    No  0.228193786  0.2253459925 -0.5795073904 -0.0793405118
## 228   Yes -1.596508547  0.0295784817 -0.6056158500  0.1037918152
## 229    No  0.398788586  0.1241573658 -0.8105444719 -0.1022103553
## 230    No  1.111447309  0.4455405776 -0.3255027070  0.0133837444
## 231    No  2.117501542  0.3529008021 -0.7076855529  0.1225981484
## 232    No  1.498031583  0.4197788527 -0.4531453294  0.0560318906
## 233   Yes -1.110615378 -0.2914129412 -1.3219622981 -0.2342060677
## 234    No -0.109889215  1.3687443639  1.7339568379 -0.6157043463
## 235    No -1.259735971  0.7380548960  0.7144798989  0.0288177021
## 236   Yes -1.569694178  0.0533592709 -0.5645447151  0.1095269744
## 237    No -1.736715414  0.4334828801  0.2079631089  0.2798356677
## 238    No -0.556239678  0.0983477216 -0.6725700581 -0.0905616816
## 239   Yes -0.172771995 -2.6293290682 -0.1287758406 -0.2231354206
## 240    No -1.764254088  0.6163735139  0.5714896861  0.2542350036
## 241    No  2.350509329  0.8383263298  0.1945646752  0.1556186197
## 242    No  3.159196787  0.6534789720 -0.3314436098  0.3853097943
## 243    No  0.536800409  0.4483426295 -0.2057215818 -0.0231087781
## 244    No  2.494646248 -1.7369652257  1.0802908006  0.1765545455
## 245    No -0.892448846 -2.1795844343  0.8862073997  0.0798354555
## 246    No -0.896128512 -2.5369476482  0.1922512834 -0.1061207417
## 247    No  0.189676268  0.5276751296  0.0200411882 -0.1217297378
## 248   Yes -0.429468453 -2.3550965858  0.4551416994 -0.0860768583
## 249   Yes -1.706412954  0.1021836845 -0.4435851058  0.1802437173
## 250    No  1.275306480  0.2403067352 -0.7594079157  0.0279936824
## 251    No  1.483814874  0.4271081000 -0.4346399995 -0.0084566489
## 252   Yes -1.300333090 -0.1206287598 -0.9541138726 -0.0688725466
## 253   Yes -1.602638415 -2.1990955930  0.9836529910  0.3022055433
## 254    No  0.317688173  0.2135916876 -0.6196463953 -0.1038907931
## 255    No -1.925680891  0.5359758487  0.4439505724  0.3606249188
## 256    No  1.147868075  0.9794257041  0.7142950676 -0.1408430984
## 257    No  2.752892848  0.4145319701 -0.7161586453  0.2842271975
## 258    No  2.138312705  0.2341974348 -0.9444156470  0.1489423118
## 259   Yes -1.738525078  0.1593796963 -0.3261515500  0.2144690940
## 260    No -0.543376534 -1.8502720307  1.4629106914 -0.0086038779
## 261   Yes -1.515062327 -2.1805409974  1.0031988465  0.2751398912
## 262   Yes  0.136554351 -2.7245267379 -0.3737223321 -0.3302165518
## 263    No  1.891387507 -1.8372129978  1.0067539733  0.0228449284
## 264    No -0.576583362  0.5261892468  0.1668478114 -0.0428761415
## 265    No  1.787988537  0.1515411187 -1.0342479626  0.0289530132
## 266    No  1.886173788  0.6495080039 -0.0821100316  0.1216416303
## 267    No -0.642898886  1.0254941938  1.1612735142 -0.2882394382
## 268    No  0.428243968 -2.6017159785 -0.1932607124 -0.2359228235
## 269   Yes -0.555691572  1.1957047299  1.4804348766 -0.4596317730
## 270    No -0.019705730  1.3191451721  1.6185479057 -0.5861121032
## 271   Yes  0.045191278 -2.5442699265 -0.0059588679 -0.2038939655
## 272    No  0.734348784  0.8244367404  0.4927020746 -0.1270427412
## 273   Yes -2.098928694  0.3614879802  0.1350961236  0.4532862247
## 274    No  0.531953653 -2.6048137871 -0.2199435431 -0.2294394239
## 275   Yes -1.341993078 -0.1385598827 -0.9808449419 -0.0732546949
## 276   Yes -0.915016951 -0.2367995844 -1.2538803707 -0.2322425521
## 277   Yes  1.984786439  0.3544633382 -0.6791849697  0.1590628929
## 278    No -0.369501616 -2.1650664441  0.8135047098 -0.0252811510
## 279    No -1.096447796  0.2249318344 -0.3211882321  0.0418478827
## 280    No -1.526109774  0.1386986791 -0.4067317701  0.1288978545
## 281    No -1.406045462  0.1040914395 -0.4970076335  0.0770559889
## 282    No -1.328385636  0.2049562234 -0.3154234579  0.0892687654
## 283    No -2.089012507  0.3549371349  0.1204768084  0.4463883088
## 284    No  0.967514972  1.0307946869  0.8524278856 -0.2387675415
## 285   Yes -0.061965617 -0.1232615015 -1.2012086345 -0.1964883702
## 286    No -0.280762554  0.1371219899 -0.6518316732 -0.0604244386
## 287    No -1.087855913  0.4235769437  0.0646265382  0.0809585337
## 288   Yes -1.351909265 -0.1320090373 -0.9662256266 -0.0663567789
## 289   Yes -0.722508773 -2.4635668816  0.3008360504 -0.0792365341
## 290   Yes -1.449667016  0.2719624485 -0.1616277442  0.1438970973
## 291   Yes -0.012310872 -2.2341525439  0.6095567376 -0.1044532038
## 292    No -0.156304632  0.4727746892 -0.0192759147 -0.1055974200
## 293    No -0.037168857  0.0378186281 -0.8919806365 -0.1598529021
## 294    No -0.538131197 -2.6530869456 -0.1030717405 -0.2216367245
## 295    No -1.874672271  0.5639247859  0.4892568471  0.3255218118
## 296    No -2.174126447  0.4111652243  0.2459592644  0.5055954209
## 297    No  1.892157482  0.9037645353  0.4162222599  0.0059531486
## 298    No  1.137964837 -2.2954097083  0.2621832177 -0.0871714166
## 299    No  0.461889938  0.4303259707 -0.2254806539 -0.0543625076
## 300   Yes -1.292412142 -0.1713141095 -1.0539415182 -0.1077442748
## 301    No -0.517387135  0.2601003005 -0.3650759843 -0.0411241695
## 302   Yes -0.534272919 -2.7521815565 -0.2958153663 -0.3038339322
## 303    No -0.869454569 -0.3060147613 -1.3971188350 -0.2829296758
## 304    No  1.184296677  0.9840072147  0.7166931001 -0.1709281711
## 305    No  0.571289095  0.3303211360 -0.4426075686 -0.0539457459
## 306    No -0.589184662  1.0531645389  1.2054679715 -0.3218034781
## 307   Yes  0.321175896 -2.0959817072  0.8132963027 -0.0811981265
## 308    No -0.050346927  0.2413284632 -0.4922180605 -0.1271781245
## 309    No  1.299967751 -2.2489555526  0.3204370747 -0.0609621119
## 310    No  0.905048451  0.5124446710 -0.1521578007 -0.0702122786
## 311    No -2.190653425  0.4220832999  0.2703247899  0.5170919475
## 312    No -0.039180670 -0.0016741087 -0.9683342862 -0.1813149032
## 313    No  1.731201079  0.1015398940 -1.1203644376  0.0094165355
## 314    No -0.951062247 -2.4557965553  0.3602606357 -0.0358880356
## 315   Yes -0.988780961 -0.1836011678 -1.1366105666 -0.1707988476
## 316    No  2.060995141  0.2896073973 -0.8206873361  0.1428484929
## 317    No -0.199582997  1.3512786629  1.7184206531 -0.6575697812
## 318   Yes  0.522109306  0.3438924765 -0.4061758341 -0.0626311012
## 319   Yes  0.414408076 -2.3996898368  0.2023349615 -0.1374390169
## 320    No  0.687022178  0.1906837978 -0.7381455283 -0.0686119253
## 321   Yes  1.536586078 -1.8175455169  1.1159556610 -0.0081216762
## 322    No  1.315341185  1.0440340258  0.8089500290 -0.2084828619
## 323    No -1.768389124  0.1431264680 -0.3522143853  0.2233556922
## 324    No -1.415338168  0.2177355368 -0.2738753697  0.1181826205
## 325    No  1.222586093  1.0021223425  0.7444983167 -0.1688330830
## 326    No  1.805900140  0.3601999299 -0.6298596247  0.0285458874
## 327    No -0.438710303 -2.5066029919  0.1623103123 -0.1582251080
## 328   Yes -1.061712015 -2.5128591201  0.2707585178 -0.0449498674
## 329    No -0.787641432 -1.7736213217  1.6600086224  0.0389216600
## 330    No -0.135536917 -2.4040524750  0.3016745608 -0.1006573534
## 331    No -1.198343873  0.8732217171  0.9679213038 -0.0336444753
## 332    No -1.990778442  0.5166379974  0.4180875831  0.4039496039
## 333    No  1.335829067  0.3407241997 -0.5749992902  0.0254425690
## 334   Yes -1.025166682 -0.0805085665 -0.9292634528 -0.1056338007
## 335   Yes -1.132206039 -0.2320568746 -1.2026676185 -0.1866412005
## 336   Yes  1.778571815  0.8628705194  0.3581810375  0.0311976163
## 337   Yes  1.522412449  0.2105014006 -0.8677887062  0.0889684849
## 338    No  2.226159230  0.7626655930  0.0710597684  0.1630947979
## 339    No  0.858588810  0.1806520293 -0.7926115113 -0.0234079373
## 340   Yes  2.491325846  0.5512752238 -0.3963241706  0.2450262429
## 341    No -0.144465070 -1.8935202412  1.2992788312  0.0042844261
## 342    No  2.277300407  0.8298399553  0.1926132340  0.1473397986
## 343    No  1.370391266  0.8969021364  0.5077062067 -0.0797269740
## 344    No -0.379837665  1.2428654344  1.5385426678 -0.4904084710
## 345    No -1.018866996  0.9495524213  1.0838320596 -0.1347741472
## 346    No -1.075427800 -2.5473822049  0.2063927293 -0.0645336562
## 347   Yes -0.969489948 -0.3389470909 -1.4414071844 -0.2984616041
## 348    No -0.244584145  1.3414970858  1.7079464593 -0.6461536992
## 349    No -0.989634656  0.4576413491  0.1129417553  0.0279008502
## 350    No  2.602197147 -1.7655175176  1.0012882013  0.2678044598
## 351    No -0.010310742  0.4910140263 -0.0128668720 -0.0865079640
## 352    No -1.223173899  0.3729571850 -0.0072966937  0.0667137467
## 353    No -0.516709345 -2.6380345635 -0.0774871510 -0.2400195824
## 354   Yes -0.955977575 -0.2440160844 -1.2603304053 -0.2117684069
## 355   Yes -0.888255721 -1.9330069696  1.3673233632  0.0847003562
## 356   Yes -0.756135568 -0.0991073777 -1.0180222137 -0.1410595121
## 357    No -0.789894582 -2.1276540800  0.9676603805  0.0707649002
## 358    No  2.607862820  0.5526557979 -0.4172199881  0.2719559099
## 359   Yes -0.942772675 -1.7367042099  1.7622139361  0.0678661037
## 360    No  1.163010501  0.2495443408 -0.7176960607 -0.0411578990
## 361    No -2.065476607  0.4646893099  0.3306221047  0.4353281796
## 362    No  1.151186059  0.2159537335 -0.7806896171 -0.0571098464
## 363    No  0.438417864  0.9170853846  0.7343501699 -0.2240971854
## 364    No -0.854009680  1.0251304827  1.2014448021 -0.2493400312
## 365    No -0.492185858  0.0709693990 -0.7385213106 -0.1012495849
## 366   Yes -0.708337001 -0.3546858406 -1.5230217082 -0.3337230227
## 367    No -0.627774818  0.3100795816 -0.2460856266 -0.0163638036
## 368    No -2.192306123  0.4231751074  0.2727613424  0.5182416002
## 369    No  2.700440177  0.7188596027 -0.1098089548  0.2351890231
## 370    No  3.286207534  0.6264310513 -0.4102745362  0.4258828648
## 371    No -1.245912508  0.8378007375  0.9076288402 -0.0127240863
## 372   Yes -1.042774548 -0.2863439279 -1.3253753105 -0.2379829831
## 373    No -1.164255026  0.5642283833  0.3551365869  0.0597816603
## 374    No  1.985072659  0.4622352931 -0.4678265785  0.1248589026
## 375    No  0.925935526  0.1823335258 -0.8023779575 -0.0352624144
## 376    No  0.888440164  0.3790671550 -0.4103183858 -0.0374628630
## 377    No -2.089838856  0.3554830387  0.1216950846  0.4469631351
## 378   Yes  0.483999792 -0.1101766826 -1.2830624360 -0.2166855878
## 379    No  1.848300681  0.6235539657 -0.1234732667  0.0324049374
## 380    No -0.328025642 -0.0589992553 -1.0230566250 -0.1945401398
## 381    No  0.767308022  0.3285381290 -0.4836338028 -0.1098213433
## 382   Yes -1.671706299  0.0792557257 -0.4947527092  0.1561010114
## 383    No  1.770465319 -1.3817545135  1.9233736188 -0.0869472378
## 384   Yes -1.007321763 -0.3596509138 -1.4742468322 -0.3060593591
## 385    No  1.782055683  0.2477500789 -0.8450827546  0.0332415316
## 386   Yes -1.653232760 -1.8440816964  1.6862546811  0.3695883649
## 387   Yes  1.759745750 -1.8162578385  1.0720029276  0.1041432013
## 388    No -0.006995568  0.6450578641  0.2875536744 -0.0830623084
## 389    No  1.113139875  0.3500553574 -0.5123779481  0.0073342100
## 390    No -1.781610707  0.1518609285 -0.3327219650  0.2325529135
## 391    No  0.386039297  0.0186565301 -1.0134188985 -0.1425571166
## 392    No  0.369844689 -2.2671786883  0.4690123459 -0.0818302320
## 393    No -1.499091860 -2.2294179098  0.9050922904  0.2468270707
## 394    No -1.669436800  0.6559247452  0.6309978667  0.2108874976
## 395    No  1.350609046 -2.1234057787  0.5548894704 -0.0144542399
## 396    No  2.158696031  0.7091554755 -0.0194567472  0.1270365872
## 397    No  1.314538651 -2.4097434649  0.0033185258 -0.0653494020
## 398   Yes  0.173450140  0.3411497987 -0.3425037479 -0.0697831235
## 399    No -0.130133918 -1.8814668035  1.3206664708 -0.0265875066
## 400    No -1.562150792  0.7066010491  0.7105230926  0.1330687388
## 401    No -1.301600987  0.8318065300  0.9066699229 -0.0012949163
## 402    No -1.886748566  0.5482114081  0.4604064130  0.3499040321
## 403   Yes  2.680816993  0.6867502319 -0.1697834117  0.2860396941
## 404    No  1.037622041  1.0215270062  0.8197118475 -0.2035332909
## 405    No -1.634917983  0.6728400839  0.6573243924  0.2072368508
## 406    No -0.145573011  1.3696395983  1.7433211662 -0.6423043537
## 407    No  2.064404873  0.5686455348 -0.2760269549  0.1509876815
## 408    No  0.791862939 -2.2818026875  0.3579617558 -0.1249001503
## 409   Yes -2.179910889  0.4149865507  0.2544871983  0.5096192052
## 410   Yes -2.184868983  0.4182619734  0.2617968560  0.5130681632
## 411   Yes -0.832954966 -2.6169266825  0.0247087122 -0.1670848381
## 412    No -0.778633681  0.9747519171  1.0877272106 -0.2333953894
## 413    No -0.032724793  0.2517964522 -0.4760387138 -0.0893035393
## 414    No  1.341582038  0.4884803335 -0.2870915288  0.0165868917
## 415    No  0.975572007 -1.7968815708  1.2668712029  0.0068251971
## 416    No -0.632027926  0.0675374929 -0.7180149972 -0.0818277592
## 417    No  2.648422726  0.7014455386 -0.1333315034  0.2236692621
## 418    No -0.921588574  0.8936645264  0.9549090782 -0.1137489729
## 419   Yes -0.144214218  0.0596819057 -0.8287992034 -0.1264622924
## 420   Yes -1.022541469 -2.5823200469  0.1284230478 -0.1013225414
## 421    No -1.984879235  0.4217511440  0.2314506460  0.4026319387
## 422    No -1.088903843 -0.0364990401 -0.8316670491 -0.0569809363
## 423    No  0.579968278 -0.0007365951 -1.0890552880 -0.1703390343
## 424    No -0.791065474  0.9376944561  1.0167743456 -0.1879945876
## 425    No -1.513035429  0.3180147661 -0.0602151856  0.1974778023
## 426    No  0.622222000 -1.5295732620  1.8627626348 -0.1584672013
## 427    No  2.155542216 -2.0487473041  0.5393127103  0.1036381231
## 428    No -0.659936889 -0.1610566471 -1.1567926986 -0.2043457347
## 429    No -0.490696660  0.0751619062 -0.7308464173 -0.0905483463
## 430    No  1.112469866  1.0009916308  0.7644927777 -0.1900446782
## 431   Yes -0.485346062  1.2237504260  1.5217762220 -0.4790010482
## 432    No  1.550248609  1.0084496208  0.6906882065 -0.1006980939
## 433    No -1.583558920  0.0639925857 -0.5412934639  0.1225137860
## 434   Yes -1.371043561  0.2945511629 -0.1324683427  0.1187958195
## 435    No -1.017025873  0.9564487732  1.0965872433 -0.1176596415
## 436    No -0.875376170  0.5085827657  0.1899974201  0.0259784672
## 437    No -1.164910240  0.8740599808  0.9638242302 -0.0746202140
## 438    No  3.408500081  0.6245864092 -0.4400342944  0.5198183099
## 439    No  0.638502621  0.2056759448 -0.6991462151 -0.0735459128
## 440    No -1.598987594  0.0312161930 -0.6019610212  0.1055162942
## 441    No  0.211180231 -0.3392982068 -1.6747279712 -0.3277936447
## 442    No  1.941101101 -2.0601998743  0.5590539211  0.1147217859
## 443    No  2.308994549  0.2919010370 -0.8650943459  0.1379217428
## 444    No -0.732085263  0.1841304078 -0.4712618377 -0.0371362459
## 445    No  0.443198603  0.3126380992 -0.4517976587 -0.0574094940
## 446   Yes  2.403876406  0.4776093588 -0.5224646571  0.2169309421
## 447   Yes -1.359346405 -0.1270959033 -0.9552611401 -0.0611833419
## 448    No -0.573228064  1.0521170270  1.2000464619 -0.3113763418
## 449    No -0.591232088 -0.2867533777 -1.4141775823 -0.2948348188
## 450    No  3.021994943  0.6830579553 -0.2455994728  0.3422993016
## 451    No -0.197906966  1.2223658500  1.4618922107 -0.4606247013
## 452    No -0.209341868 -2.1966241595  0.7204398777 -0.0380387927
## 453    No  0.848218582  0.8627173863  0.5456990388 -0.1579850044
## 454   Yes  0.066115975  0.1755639511 -0.6440909327 -0.1131558173
## 455    No -0.336113247  1.1786331612  1.4037213320 -0.4615705502
## 456    No  0.427460789 -0.1169553180 -1.2853346237 -0.2077174875
## 457    No  0.415018801  0.0679562601 -0.9241517468 -0.0772211680
## 458    No  0.148720263  0.2093340557 -0.5944646030 -0.1097096185
## 459    No -2.150278386  0.4272261649  0.2729463859  0.4914460510
## 460    No -1.267621674 -0.1876912229 -1.0904898064 -0.1249890647
## 461    No -2.046673375  0.4840133358  0.3649139703  0.4245302034
## 462    No -0.390588782  0.2271143799 -0.4537052794 -0.0838868528
## 463   Yes -0.686440899 -0.4226232641 -1.6587452354 -0.4005008711
## 464   Yes -0.556957327 -0.3582375903 -1.5593205729 -0.3597232511
## 465    No  3.664449559 -1.7923804047  0.7339511122  0.5015545866
## 466    No  0.522505972  1.1772706394  1.2301852470 -0.4030795561
## 467    No  2.716104695 -1.8169864605  0.8787019765  0.2424903866
## 468    No  2.469786466  0.8141590330  0.1228861750  0.1965185902
## 469    No -0.955326849  0.9912891509  1.1542192917 -0.1982604541
## 470   Yes -1.114668310  0.2003831248 -0.3655677951  0.0412665286
## 471    No -1.471717864 -1.7714417761  1.7946903586  0.2617250699
## 472   Yes -1.599813943  0.0317620968 -0.6007427449  0.1060911205
## 473    No -1.025952606 -0.0114954697 -0.7945398509 -0.0891807614
## 474    No -0.734317916  0.3885337095 -0.0721442981  0.0063462085
## 475   Yes -1.274232466 -0.1833239927 -1.0807435962 -0.1203904541
## 476   Yes -0.143678059  0.1189313633 -0.7129770338 -0.1310873587
## 477    No  0.536500814 -2.0525579928  0.8543294070 -0.0190788094
## 478    No -0.982752463 -0.0990229430 -0.9736689842 -0.1135848463
## 479   Yes -0.726151046 -0.3519121990 -1.5139101565 -0.3417264690
## 480   Yes -0.781912460  0.0932588786 -0.6382840532 -0.0740598282
## 481    No -1.896698650  0.5521036461  0.4699634540  0.3507464167
## 482   Yes -0.082609785  0.8158024990  0.6382360894 -0.1747758820
## 483    No -0.028423837 -2.3448391950  0.3960366812 -0.0895563879
## 484    No  3.184114370  0.6663115833 -0.3123208028  0.4343994170
## 485   Yes -0.796080886 -0.1672797593 -1.1424023339 -0.1882858623
## 486    No  2.252905439  0.8523075736  0.2421691834  0.1090109385
## 487    No -0.154616411 -0.2308395468 -1.3908982002 -0.3056519804
## 488    No  2.340036838  0.8102988297  0.1433678740  0.0836645424
## 489   Yes -1.280016908 -0.1795026662 -1.0722156623 -0.1163666697
## 490    No  2.512396435  0.5356958751 -0.4305530109  0.2266058228
## 491    No -1.494985556  0.0029490050 -0.6767006534  0.0551632265
## 492   Yes -1.237622292 -0.1647842795 -1.0517684192 -0.1186799220
## 493    No  1.267859891 -1.5461613875  1.7014599257 -0.0962765962
## 494    No -2.171647400  0.4095275129  0.2423044356  0.5038709419
## 495   Yes -1.058855892  0.4543663216  0.1200718340  0.0346380592
## 496    No -0.388707308  0.3782372678 -0.1600257651 -0.0185136216
## 497    No -0.211680600  1.3415332719  1.7009548083 -0.6196723752
## 498   Yes -1.676064236 -2.0162240967  1.3540320509  0.3791472849
## 499   Yes -0.281294057 -0.2709420243 -1.4446207224 -0.2891167139
## 500    No  1.257730880 -0.0658941382 -1.3513446892 -0.1228030889
## 501    No  2.278696143 -1.5297894937  1.5305557843  0.0548529850
## 502    No  1.434933438  0.9733438419  0.6455342650 -0.1334176019
## 503    No  1.268504013  0.5312244136 -0.1884248203 -0.0148250648
## 504    No  1.920925370  0.8440392592  0.2932045296  0.0330106199
## 505   Yes  0.209019199 -2.4789164457  0.0894203126 -0.2030676589
## 506    No -0.768218171 -0.0616194782 -0.9424670052 -0.1354517117
## 507   Yes -0.907988452 -0.3806208401 -1.5340698833 -0.3436118700
## 508   Yes -0.942389187 -0.1663238727 -1.1121416212 -0.1641028188
## 509    No -2.180737238  0.4155324545  0.2557054746  0.5101940316
## 510    No  0.222646044 -2.4796319030  0.0851319122 -0.1937568110
## 511    No  2.407741051  0.4802126479 -0.5168510017  0.1562334800
## 512   Yes -0.871838925 -2.5108722067  0.2382397447 -0.0972081984
## 513    No  2.166835286  0.4124569284 -0.6017499108  0.1578198741
## 514    No  0.518969956  0.0735808325 -0.9327752879 -0.1204672765
## 515   Yes  1.275796804  0.1447137337 -0.9447518034 -0.0489658882
## 516    No -0.565077168  0.4407247539 -0.0030253423 -0.0183301915
## 517    No -0.950971276 -2.4650718654  0.3425545501 -0.0568466149
## 518   Yes  0.104039221 -2.1776060385  0.6968515989 -0.0919880235
## 519    No -1.855949878  0.5619437973  0.4814618413  0.3360513707
## 520    No  2.726633388  0.5956142245 -0.3563548668  0.2555524148
## 521    No -0.374523696 -1.9138287633  1.3054844333 -0.0172428817
## 522    No  1.472148386  0.5690059691 -0.1556439438  0.0251292071
## 523   Yes -0.271709891  0.1530687225 -0.6218874377 -0.0867034619
## 524   Yes  0.873523356  0.0944115336 -0.9632211678 -0.0675719682
## 525    No  1.504387949  0.4692410532 -0.3572348641  0.0338841150
## 526    No  3.657915782 -1.7893291126  0.7411715082  0.5032311263
## 527    No  1.897145736  0.5354393211 -0.3064122557  0.0808995548
## 528    No -1.217553028  0.8738065742  0.9731585577 -0.0477302733
## 529    No  2.257587627 -1.9278276712  0.7539055291  0.1808899573
## 530    No -1.500482593  0.7107920465  0.7067604040  0.1223484965
## 531    No -0.218434082  1.3372554018  1.6942467846 -0.6347908280
## 532    No -1.137368632 -0.2241664155 -1.1865139261 -0.1728918208
## 533    No  3.132456689 -1.7873653189  0.8517569544  0.3649002674
## 534   Yes -1.104004587 -0.2957801715 -1.3317085083 -0.2388046784
## 535    No -0.508759846 -0.1686178984 -1.2006935732 -0.2395999977
## 536    No  1.681474070  0.7260052685  0.1106418290 -0.0085398809
## 537    No -0.265534027  0.4750241259  0.0054947675 -0.0487320175
## 538    No  2.542959902  0.7175629035 -0.0814462170  0.2453008437
## 539    No  1.573912241  0.6952563537  0.0706530929  0.0445414502
## 540    No  3.329555277  0.6259625162 -0.4204697944  0.4595993658
## 541    No -1.149886328  0.1368638489 -0.4820895853  0.0083838179
## 542    No -2.185695331  0.4188078772  0.2630151322  0.5136429896
## 543   Yes -0.665396450 -0.1631601264 -1.1596321568 -0.2134956610
## 544   Yes -1.323252191  0.3087103092 -0.1142455534  0.1195444407
## 545    No  0.290128469  0.2914018738 -0.4624028324 -0.0889717641
## 546   Yes  0.702260442  0.2992556891 -0.5284702887 -0.0890057069
## 547    No  2.604507411  0.5641837788 -0.3930390173  0.2257021801
## 548    No  2.025966641 -2.0434209587  0.5743165887  0.1511561407
## 549    No -1.779151384  0.6049029925  0.5513350633  0.2859744556
## 550    No  3.202674133  0.6450675148 -0.3568125881  0.4011198728
## 551    No  3.362025767  0.5974089062 -0.4818847834  0.4209064894
## 552    No -0.631283339  1.1475463826  1.3989098473 -0.3506745807
## 553    No -1.443220224  0.6498755796  0.5768356227  0.0998656887
## 554   Yes  0.252550667  0.2487772204 -0.5385754710 -0.0763696748
## 555    No  0.961174074  0.7279292959  0.2585249782 -0.0941830860
## 556    No -2.179910889  0.4149865507  0.2544871983  0.5096192052
## 557    No  0.263281260  0.4357845112 -0.1754111369 -0.0619315910
## 558    No -0.921399911  0.0200890789 -0.7537908635 -0.0730805508
## 559    No -1.694017720  0.0939951278 -0.4618592498  0.1716213223
## 560    No  2.229702111  0.3975152459 -0.6437317244  0.1743794328
## 561    No -2.054286986  0.4024636418  0.2066085748  0.4426126170
## 562    No -1.091137141 -0.0348263727 -0.8279982987 -0.0549800251
## 563    No  2.122587928  0.5131676009 -0.3957788717  0.1415753188
## 564    No -1.199117557  0.0214663442 -0.6974857740 -0.0139726728
## 565    No  1.673845329  0.9417095077  0.5354241958 -0.0831643143
## 566    No -0.053270584 -0.2396443997 -1.4294351101 -0.2443047012
## 567    No  1.827997486  0.9284739694  0.4771071436  0.0105042169
## 568   Yes  0.913308574  0.1067684114 -0.9467170113 -0.0773334725
## 569    No -1.502850478  0.3327956664 -0.0327369836  0.1694637405
## 570    No -0.533484371  1.2095419299  1.5035337787 -0.4801399267
## 571    No  0.544662525 -1.7209054063  1.5027342681 -0.0969280354
## 572    No -1.025617080  0.0755901997 -0.6255953298 -0.0308487862
## 573   Yes  1.995752636  0.4564565383 -0.4811375369  0.1203244920
## 574    No  1.074332370 -2.5032740987 -0.1308792095 -0.1216458624
## 575    No  1.546446407  0.6947299827  0.0770220702 -0.0483896148
## 576    No  0.657681147  0.0621928273 -0.9827770719 -0.1046992050
## 577    No -1.008960174 -0.0150494268 -0.8049630351 -0.0836058633
## 578    No  1.015632917 -2.2298798083  0.4133892419 -0.0367334917
## 579    No -2.155730345  0.4310947850  0.2814931548  0.4958438319
## 580   Yes -1.882222441  0.5721390745  0.5065403730  0.3380898602
## 581   Yes -1.264316279 -0.1898748380 -1.0953629115 -0.1272883700
## 582   Yes -0.650186458 -2.6857386845 -0.1442457443 -0.2461762482
## 583    No -2.194785170  0.4248128188  0.2764161712  0.5199660792
## 584    No -2.120650619  0.4407919984  0.2939354822  0.4762762714
## 585   Yes -0.850660892 -2.6958680332 -0.1249784168 -0.2208864184
## 586    No  0.646164920  0.7186945199  0.3025968154 -0.0890576214
## 587    No -2.066710087  0.4658407485  0.3330824057  0.4369493931
## 588    No  2.864111448  0.7448577721 -0.0938772496  0.3557554938
## 589    No  2.481246350  0.7971493956  0.0865134335  0.2368451888
## 590    No  3.258766168  0.6318159490 -0.3941178360  0.4160761643
## 591    No -0.739914165  0.9742884937  1.0785348542 -0.2033806311
## 592    No  1.830504634  0.7213294677  0.0697458803  0.1004284995
## 593    No  0.225588535  0.1738268073 -0.6786662511 -0.1285483559
## 594    No -1.755167541  0.1343920076 -0.3717068057  0.2141584709
## 595   Yes -1.050844002  0.1244773357 -0.5254829700 -0.0099394510
## 596    No -1.011641489  0.2576882687 -0.2739673362  0.0447623361
## 597    No -1.307500380 -0.0385909949 -0.7931849131 -0.0280062689
## 598    No  1.431220027  0.4614239571 -0.3579188942  0.0271557634
## 599    No -0.310959295  1.2726927788  1.5835961660 -0.5069150169
## 600    No -0.618218890  0.0522521294 -0.7501250237 -0.1054076855
## 601    No -2.148285852  0.4281730361  0.2743243504  0.4951917175
## 602    No  1.582172879  0.8367979518  0.3476514870 -0.0460946531
## 603    No  1.697947741  0.2097854109 -0.9023847965  0.0190778336
## 604    No  1.019238499 -0.0296192361 -1.2339546952 -0.0924963473
## 605    No  2.277235189  0.8272401224  0.1891486453  0.0716913492
## 606    No  0.541065110  0.3373005640 -0.4228132369 -0.0623694426
## 607    No  0.088344264  0.8343382509  0.6413331292 -0.2046892586
## 608    No  3.369738816  0.6124384117 -0.4548809847  0.4611739286
## 609   Yes  2.861716043 -1.8287198570  0.8265609058  0.2630114464
## 610   Yes -1.768292598  0.4149956299  0.1780079596  0.2822821784
## 611   Yes -1.079432495  0.0479054609 -0.6697955195  0.0026014287
## 612    No -0.302328719  1.2812815617  1.5996005170 -0.5502166827
## 613    No  1.900456036 -2.2222074274  0.2514583020  0.0632679446
## 614    No  0.724000688  0.6281323774  0.1102487099 -0.0925537933
## 615    No -1.214170222  0.2991419913 -0.1529405607  0.0459653493
## 616    No -1.885499395  0.4513362250  0.2709758768  0.3403470408
## 617    No  2.900554160 -1.7819984831  0.9087960118  0.3304108207
## 618    No  1.600556406  0.5787728150 -0.1616169279  0.0108979220
## 619    No -0.945466070 -0.1315356478 -1.0436667744 -0.1573909752
## 620    No -1.396189849 -2.0105968858  1.3120994846  0.2679512518
## 621    No  2.039311129  0.6282299871 -0.1540661748  0.1265587455
## 622    No  0.730658097  0.3292327082 -0.4759236650 -0.0679504223
## 623    No -1.638517480  0.6723280793  0.6571204828  0.2031879319
## 624   Yes -2.007603845  0.4942780724  0.3775823180  0.4094506014
## 625    No  0.275487690 -0.0098006453 -1.0469171901 -0.1563791411
## 626    No -0.070682533  0.0668872982 -0.8293596549 -0.1208291101
## 627    No  2.883492436 -1.8076460256  0.8635513765  0.2585665528
## 628    No  3.459590282 -1.7631369929  0.8336737304  0.4035000740
## 629   Yes  1.603114530 -1.9556835434  0.8308775158  0.0805359074
## 630   Yes  1.843248199 -2.2523018254  0.2048701277  0.0188314321
## 631    No  0.124450836  0.6978439314  0.3659173970 -0.1367127807
## 632    No  2.464690667  0.8114438502  0.1188022352  0.1862734946
## 633    No -1.922404657  0.5298074069  0.4314852843  0.3492667075
## 634    No -0.088247863  0.6174510895  0.2493897309 -0.0714485531
## 635   Yes  2.681607106  0.5691796817 -0.4000571567  0.2988891466
## 636    No  0.688451585  0.0479932180 -1.0164564209 -0.1122086828
## 637    No  1.588390422  0.9008362273  0.4713860351 -0.0353028724
## 638   Yes  2.358637105 -1.9751545714  0.6419766979  0.1546515517
## 639   Yes -0.672257476 -0.1535209188 -1.1397794143 -0.1971437234
## 640    No -0.101957181  1.2641317404  1.5268592720 -0.5677429452
## 641   Yes  0.082126335  0.6485098439  0.2764906041 -0.0734315177
## 642   Yes -1.028806835 -0.3454574155 -1.4425716491 -0.2911138745
## 643    No  1.524682283 -1.9641862252  0.8314947243 -0.0016717424
## 644    No -1.665774215  0.5480510351  0.4185980847  0.2480289767
## 645   Yes  0.250225114 -2.4790261952  0.0803688095 -0.1702560569
## 646   Yes -1.753514843  0.1333002000 -0.3741433582  0.2130088182
## 647    No  0.733360701  0.6274734379  0.1069836842 -0.0865381702
## 648   Yes -0.744266292 -2.7218045559 -0.1957872462 -0.2640351449
## 649    No -0.105608419 -2.1664830361  0.7586122782 -0.0258688176
## 650   Yes -1.269632476 -0.0956317315 -0.9115574955 -0.0572615668
## 651   Yes -1.275885164 -0.1822321851 -1.0783070437 -0.1192408014
## 652    No -1.218584626  0.8670253718  0.9604492332 -0.0639341788
## 653    No -1.604284883  0.5814714629  0.4720886173  0.2337412753
## 654   Yes -1.741017171 -1.8806422082  1.6309401747  0.4253599029
## 655    No -0.509481193 -0.2610660198 -1.3797806589 -0.3104007714
## 656    No  2.232972153  0.7543464360  0.0537344779  0.1496974528
## 657    No  0.812972782  0.4706296311 -0.2165710240 -0.0297982459
## 658   Yes -2.153321210  0.4287836828  0.2765692771  0.4925363620
## 659    No -1.156729662  0.8912095581  0.9962492396 -0.0988715058
## 660   Yes -2.018932848  0.4082192097  0.2114759164  0.4143276257
## 661    No -1.445108950  0.2673032317 -0.1714902402  0.1369894646
## 662    No -2.177431842  0.4133488394  0.2508323695  0.5078947262
## 663    No  1.367403811  0.8592609603  0.4350925529 -0.0977733814
## 664    No -0.579147415  1.1716749926  1.4366894521 -0.3935357362
## 665    No -1.180627555 -0.1519698011 -1.0380846180 -0.1135962329
## 666   Yes -1.313089719 -0.1124916092 -0.9358602014 -0.0606566696
## 667    No -0.505065310  0.9654233043  1.0156716335 -0.2441607788
## 668   Yes -1.643976554  0.1775991819 -0.3087408866  0.1922377337
## 669    No  1.169102046  1.0337211608  0.8177081552 -0.2097959811
## 670    No -0.701617260  1.1122044242  1.3436531849 -0.3478401265
## 671    No -0.523295116  1.0619366735  1.2095349510 -0.3187492060
## 672   Yes -1.268448023 -0.1871453191 -1.0892715301 -0.1244142384
## 673    No -1.484346965  0.6446257899  0.5741714432  0.1246660278
## 674   Yes  0.430135923 -1.5517783514  1.8572033882 -0.1538286827
## 675    No  3.077450325 -1.8657046214  0.7097431120  0.3522378759
## 676    No -0.691618253  1.0045053521  1.1287478095 -0.2355177432
## 677   Yes -1.904570742  0.2671231959 -0.0850704256  0.3255529069
## 678    No -0.619702252 -0.5127103294 -1.8463272616 -0.4815243489
## 679    No  0.906755103  0.4494703300 -0.2770429071 -0.0025327888
## 680   Yes -1.186639480 -0.2411897934 -1.2098808811 -0.1813220452
## 681    No  1.390674210  0.7687721536  0.2516354903 -0.0054802042
## 682    No -1.360962414 -0.0402878268 -0.7864271725 -0.0050465637
## 683    No  1.516842469 -2.2339028159  0.3055597089  0.0077711199
## 684    No -1.333729588 -0.1440189205 -0.9930277046 -0.0790029582
## 685    No -1.684101533  0.0874442824 -0.4764785651  0.1647234063
## 686    No -0.604423912  1.0442991624  1.1903543312 -0.2844312734
## 687   Yes -1.418194032 -2.2835919274  0.7844313479  0.1888948386
## 688    No -0.389125464  1.0112963117  1.0827018384 -0.2562266775
## 689    No  1.183898927  0.5184632244 -0.1960822022 -0.0419403422
## 690    No -2.170821051  0.4089816091  0.2410861593  0.5032961156
## 691    No  0.074205758  0.2817288957 -0.4389502877 -0.0750416327
## 692    No -0.834537702  1.0279002426  1.2025478794 -0.2274368430
## 693   Yes -1.165519115 -0.1544648505 -1.0460843523 -0.1071318536
## 694    No -1.342602374 -1.6983571966  1.9137392396  0.1825298350
## 695    No -2.167515655  0.4067979940  0.2362130542  0.5009968103
## 696    No  2.317047742  0.8528065875  0.2293566606  0.1616052911
## 697   Yes -1.600302648  0.1147498462 -0.4394354471  0.1544698503
## 698    No  1.321749700 -1.9467372493  0.9053559759  0.0144780602
## 699    No  1.579207336  0.9953192003  0.6594364020 -0.1072367869
## 700    No  1.210790517  0.9292660418  0.6036672542 -0.1343938736
## 701    No  0.439287844  0.2662407856 -0.5409097678 -0.0960510437
## 702    No  0.234990959  0.1578514027 -0.7126253697 -0.0875274048
## 703    No -2.142619673  0.4210176552  0.2594642744  0.4835131502
## 704    No -1.580489627  0.1388616329 -0.3962307580  0.1553381962
## 705   Yes -0.082916959  0.1422332785 -0.6801035426 -0.0992017910
## 706    No  0.997861324  0.9387218314  0.6659107778 -0.2140900186
## 707    No  0.881378370 -2.4578046481 -0.0042496765 -0.1036552435
## 708    No  0.006018899  0.2526633607 -0.4826995236 -0.0562528850
## 709    No  0.069042241  0.1979371552 -0.6005777808 -0.1297783035
## 710   Yes -2.185695331  0.4188078772  0.2630151322  0.5136429896
## 711    No -0.274007379  0.0530352650 -0.8165792443 -0.1062673391
## 712    No -0.370339377  1.1417296028  1.3362598121 -0.3636058185
## 713    No -0.479711592 -0.0986783197 -1.0706053234 -0.1971095322
## 714    No  0.015368512  1.3182264624  1.6107485063 -0.6297554425
## 715    No  1.191172140  0.3964440509 -0.4377088509  0.0357245498
## 716    No  1.230004587  1.0457646056  0.8290831544 -0.2033252725
## 717    No  0.358314608  0.1934961176 -0.6666833808 -0.1168615425
## 718    No -0.752482592  0.4477768830  0.0476788331 -0.0132972179
## 719    No  2.179619376 -1.5672928219  1.4758666604  0.0994265889
## 720    No -2.147970441  0.4249006690  0.2680167757  0.4880247561
## 721    No -0.430995578  1.2162221541  1.4957581127 -0.4524645966
## 722   Yes -0.934586341 -0.2562325912 -1.2882156388 -0.2223063940
## 723   Yes -1.685949334  0.1662580307 -0.3228387904  0.2025472441
## 724   Yes  0.894142747 -2.2652004934  0.3691505784 -0.0748946393
## 725    No -1.680623950 -1.8839304789  1.6131892857  0.3966576355
## 726    No -1.429088383  0.6339094568  0.5418793347  0.1447022075
## 727    No -1.001909455 -0.1887858413 -1.1436797314 -0.1930882774
## 728   Yes  0.679910616 -2.2865750335  0.3699273006 -0.0861411573
## 729    No  1.543088643  0.8225504448  0.3273917753 -0.0400576963
## 730   Yes  1.049696523  0.3921795666 -0.4169607059 -0.0177531697
## 731    No -2.060438882  0.4634155536  0.3271122236  0.4364818479
## 732    No -0.186597645  0.1852052282 -0.5759142990 -0.0849492207
## 733    No  2.048719231  0.8955791003  0.3684967892  0.0433048950
## 734    No  0.247858324  0.0713168642 -0.8833521309 -0.1340167184
## 735    No -0.503075603  0.5360450217  0.1713463585 -0.0312524707
## 736    No  0.907073946 -0.0762188964 -1.3017017490 -0.1487501722
## 737    No  2.751283546  0.6855582725 -0.1856985633  0.2701728350
## 738    No  0.922089225 -1.9760377019  0.9278518384 -0.0241116165
## 739    No  2.745337154 -1.5754721202  1.3447902545  0.2559643959
## 740    No  0.426971904  0.6175377408  0.1493480543 -0.1457867757
## 741    No -1.140048192 -0.2311820295 -1.1993166068 -0.1909494481
## 742   Yes -0.411986845 -0.2929758992 -1.4615487622 -0.3045337759
## 743    No -0.302329766  1.1874193162  1.4132256794 -0.4145428661
## 744    No -1.643972230  0.2081815628 -0.2489471107  0.1918850386
## 745    No  3.428094186 -1.7563385144  0.8533959977  0.3936454341
## 746    No  3.586307177 -1.7888998191  0.7573563345  0.4467513047
## 747    No -0.944158278 -2.5491503654  0.1778102546 -0.1026244725
## 748    No -0.878537118  1.0482427045  1.2522583356 -0.2863135505
## 749    No  2.047305030  0.6652564041 -0.0836990854  0.1472279869
## 750    No -0.518047766  0.4062174657 -0.0803960985  0.0108591034
## 751    No  1.983285330  0.8529727801  0.2983366483  0.0335989639
## 752    No -1.064460315 -0.0529255034 -0.8682349912 -0.0746159835
## 753    No -0.963854549 -0.3374820463 -1.4398228535 -0.2906182365
## 754   Yes  0.298740306 -2.5252009458 -0.0180899107 -0.2360314581
## 755    No -0.345996608  1.2863486833  1.6186332586 -0.5737628477
## 756    No -2.124387321  0.4422508166  0.2975190655  0.4765860679
## 757   Yes -0.428057904 -0.0806525520 -1.0458382932 -0.1844946018
## 758    No  2.472954157  0.8059848124  0.1066194725  0.1805252313
## 759    No -2.165036608  0.4051602827  0.2325582254  0.4992723313
## 760   Yes -0.029688187 -0.0029776516 -0.9728568960 -0.1766546209
## 761   Yes -1.261342692 -0.1044042613 -0.9300642112 -0.0705020059
## 762    No  1.569625251  0.9893120871  0.6500379624 -0.1285457153
## 763    No -0.354307039  1.2731613139  1.5937914242 -0.5406315179
## 764    No -1.594732604  0.3807631152  0.0784460847  0.2045097546
## 765    No -0.287494106  0.0983480240 -0.7243230568 -0.1537444560
## 766    No -1.801751759  0.5837119553  0.5142979145  0.2894924882
## 767    No  0.501000967  0.4492214140 -0.1963638048 -0.0498388712
## 768    No -0.752287842  0.1719052450 -0.4917170020 -0.0113644777
## 769    No -1.880369068  0.5438112780  0.4506471001  0.3450452499
## 770   Yes -0.256461578 -0.1550976312 -1.2246156388 -0.2156215353
## 771   Yes -2.179910889  0.4149865507  0.2544871983  0.5096192052
## 772   Yes -0.842846817 -0.2729751119 -1.3383481659 -0.2563660230
## 773   Yes  0.653585961  0.1101683639 -0.8874586815 -0.1386034802
## 774    No  3.236907612  0.6452928753 -0.3637288991  0.4290971829
## 775    No -1.782117234  0.2195868746 -0.2005127124  0.2463115318
## 776   Yes -1.101132029 -0.2462133028 -1.2363297703 -0.1938092032
## 777    No  2.328374615  0.4429224276 -0.5738844398  0.1474032978
## 778   Yes -1.723759091  0.1515283635 -0.3442913921  0.2085134569
## 779    No  1.766798933  0.9217592201  0.4774355433 -0.0538223436
## 780    No -1.626503007  0.2007147476 -0.2669338159  0.1889701559
## 781    No -0.590954027  0.4217214443 -0.0351877482 -0.0124803322
## 782   Yes -1.646089483  0.0623327085 -0.5325192736  0.1382813951
## 783    No  0.311061105  1.0744357382  1.0691161408 -0.3179951819
## 784   Yes  1.953432764 -2.1986226649  0.2880204495  0.0198482236
## 785    No  1.157955043  1.0840108551  0.9189525063 -0.2441107897
## 786    No -0.189852042  0.4632954375 -0.0316314372 -0.0843062233
## 787    No -0.182131386  0.1380091505 -0.6683471199 -0.1186808761
## 788    No  1.658299685  0.9647724373  0.5842163662 -0.1130433018
## 789    No  0.844790437  0.8668738805  0.5543604557 -0.1513107229
## 790    No  1.718097422  0.8396726159  0.3269232479 -0.0699231335
## 791    No -1.984661766  0.5088832504  0.4019879391  0.3912734316
## 792    No  0.017621739  0.4025784924 -0.1919301933 -0.0555195966
## 793    No -1.577856377  0.2143321025 -0.2499276651  0.1891764723
## 794    No -1.402019743 -0.0528256539 -0.8030033935  0.0032839973
## 795    No  0.237963047  0.2194376944 -0.5928699404 -0.0848993476
## 796    No -1.514484261  0.6123477494  0.5161315444  0.1666985309
## 797    No -2.178258191  0.4138947432  0.2520506458  0.5084695526
## 798   Yes  2.222486439  0.5919214960 -0.2626077093  0.1911957956
## 799    No  2.097419072 -1.4979183454  1.6287497737  0.0513784138
## 800   Yes -0.398429662 -0.2903840332 -1.4595156664 -0.2877795344
## 801    No -0.995556301  0.8870605562  0.9567099166 -0.1183682895
## 802    No  0.428675364  0.6190437099  0.1503752716 -0.0713042397
## 803   Yes -0.867509713 -0.2200270682 -1.2306133233 -0.2257961353
## 804    No  1.936363311  0.9094523048  0.4190608681 -0.0153836574
## 805    No -0.919366763  0.2848725717 -0.2389742433  0.0410341867
## 806    No  3.050031277  0.6372242254 -0.3404923268  0.3305675558
## 807   Yes  1.213514445  0.1822957316 -0.8597238709 -0.0137200857
## 808   Yes -1.359346405 -0.1270959033 -0.9552611401 -0.0611833419
## 809   Yes  2.205777418  0.4658907919 -0.5052585676  0.1708220713
## 810   Yes  2.847600120  0.6594518806 -0.2561475903  0.2882541588
## 811    No -0.844588905  0.9173491609  0.9865066702 -0.1376680767
## 812    No -0.992189274  0.7532071641  0.6933554800 -0.0706712578
## 813    No -1.823130668 -1.9256843203  1.5582356836  0.4664494989
## 814    No  0.015231636  0.0931668542 -0.7947268842 -0.1317119758
## 815   Yes -1.034653249 -0.2924866378 -1.3388312167 -0.2453955409
## 816    No  2.040415272  0.4083436645 -0.5839441393  0.1167645009
## 817   Yes  0.422277993 -0.2392929241 -1.5219378020 -0.2801704929
## 818    No  2.222438148  0.7828295928  0.1132656344  0.0664286098
## 819    No  2.536566506  0.4998641083 -0.5070229305  0.3041523799
## 820    No  0.764170916  0.4403408043 -0.2668126413  0.0017697411
## 821    No  1.626584603  0.2826285120 -0.7466919579  0.0572906561
## 822    No -1.287315744 -0.0051380982 -0.7322479331 -0.0056590006
## 823    No -0.248379102  1.1818877416  1.3925796459 -0.4535007885
## 824   Yes -0.301176802 -0.1003577733 -1.1091611305 -0.1970771927
## 825   Yes -0.391736998 -2.7058426658 -0.2336039503 -0.2935048057
## 826    No -1.690154773  0.5312509038  0.3903157091  0.2600750127
## 827   Yes  1.888469307  0.6026665993 -0.1734007352  0.0869725543
## 828    No -0.611852042  0.6155715943  0.3492908063 -0.0776036313
## 829   Yes  1.991976537  0.2903418714 -0.8059552475  0.1588397365
## 830    No -0.980644345  0.8632440423  0.9066167596 -0.0907064609
## 831    No  1.775803697  0.9037369117  0.4396586320 -0.0177617544
## 832    No  0.718857287  0.2497411986 -0.6294059092 -0.0485606073
## 833   Yes -0.833687139 -2.5745070275  0.1072323590 -0.1411876764
## 834    No  2.260440877 -1.8017775193  0.9995667308  0.1901909750
## 835    No  1.337255339  0.8023705821  0.3286442865 -0.0418567368
## 836   Yes -1.774999915  0.1474936983 -0.3424681751  0.2279543028
## 837    No  0.399803256  0.3223881132 -0.4238938582 -0.0701186336
## 838    No -0.936380515  0.9873496770  1.1426417065 -0.1919920463
## 839   Yes  2.179479803 -1.9496163644  0.7276398861  0.1385179118
## 840    No  3.007587734  0.6876430897 -0.2337647485  0.3411367595
## 841   Yes -1.870374160  0.5632092709  0.4869701558  0.3273478706
## 842    No -1.620610449  0.4614663205  0.2408452781  0.2273380369
## 843   Yes -1.023022392 -0.3492787419 -1.4510995830 -0.2951376588
## 844    No -1.770685763  0.5954920279  0.5315732202  0.2714274578
## 845    No  1.904973786  0.7327121171  0.0784285267  0.0465846164
## 846    No -1.591395342  0.4257519598  0.1649955284  0.2394975009
## 847    No  2.562990804  0.7968981964  0.0699720805  0.2321600030
## 848    No  2.448714628  0.8098348109  0.1191622895  0.1698070877
## 849    No  3.439316005  0.6057491448 -0.4825666862  0.5018295425
## 850    No  1.325410808  0.5247232064 -0.2130330274  0.0160912213
## 851    No -2.064585965  0.3750610394  0.1550872316  0.4419157522
## 852    No -1.270831634 -0.0081009142 -0.7414348250  0.0008484596
## 853    No -0.237987106  1.3098001360  1.6431319218 -0.5733307816
## 854   Yes  2.361032923  0.5665144575 -0.3407851422  0.2447449196
## 855    No  2.329768106  0.8426739392  0.2073056695  0.1488355701
## 856   Yes -1.669227253  0.0776180144 -0.4984075380  0.1543765324
## 857    No  2.122174298  0.7178928761  0.0050411744  0.1175462271
## 858    No  1.525047644  1.0101725220  0.6993812932 -0.1170107675
## 859    No -1.485682414  0.7488498410  0.7791125252  0.0811161399
## 860    No  2.126009898  0.6413522184 -0.1446907270  0.0864714305
## 861   Yes -0.215244250 -2.2679155163  0.5828072098 -0.0650239194
## 862   Yes -0.830151303 -0.3721395774 -1.5331213440 -0.3316313062
## 863   Yes  0.114865431 -0.0540680727 -1.1012975681 -0.1765223549
## 864   Yes -1.039427478 -0.2001567792 -1.1587903641 -0.1792721530
## 865    No  0.189592082  1.0690363805  1.0834071178 -0.3579944511
## 866    No -2.054663910  0.4622466658  0.3236441072  0.4384648127
## 867   Yes  1.671397530  0.6340903128 -0.0683788776  0.0537645154
## 868    No -1.999511429  0.3731021012  0.1388666250  0.4199836450
## 869    No  2.731246468  0.7385640913 -0.0773672992  0.2348840688
## 870    No  1.969118266  0.4985090097 -0.3937557934  0.1246071431
## 871    No -0.337513664  1.2842380936  1.6127883704 -0.5717425031
## 872   Yes  0.535123171  0.9429095692  0.7657989874 -0.2273546168
## 873    No  1.452114263  0.2842226603 -0.7091709903  0.0603258912
## 874    No -1.865223934  0.2807446057 -0.0660609278  0.3183069556
## 875   Yes -0.025739745 -0.2781888926 -1.5088411669 -0.3096148870
## 876    No  0.496305932  0.7291602711  0.3532321710 -0.1158610197
## 877    No  1.054255883  0.8316512012  0.4422478896 -0.0631184354
## 878    No -0.411139432  0.5047346511  0.0933930243 -0.0981866131
## 879   Yes -0.214392747 -0.4181255755 -1.7425906049 -0.4297736850
## 880    No -1.238466984 -1.6361870113  2.0158575778  0.1282453932
## 881   Yes -0.888712772 -0.2038031161 -1.1951268988 -0.2060203744
## 882    No  2.972601376  0.5529783076 -0.4904362648  0.3562221762
## 883    No -0.319042954  0.9175777506  0.8845197895 -0.2033995207
## 884    No -2.177431842  0.4133488394  0.2508323695  0.5078947262
## 885    No -0.584445282 -2.5839786934  0.0401241403 -0.1717951582
## 886    No  0.945607898 -2.5262916568 -0.1486264625 -0.2074152378
## 887    No  0.730940347  0.2196145047 -0.6894456584 -0.1071777225
## 888   Yes  2.332972033  0.5665668901 -0.3331847860  0.1526488525
## 889    No  0.440689837  0.1474303782 -0.7736790271 -0.0855220156
## 890   Yes  1.744270485  0.3174712920 -0.7010693455  0.0216148380
## 891    No  0.513182458 -2.1509374044  0.6673023988 -0.0517576999
## 892   Yes -2.102234090  0.3636715954  0.1399692287  0.4555855301
## 893    No  1.657301836  0.7272110534  0.1181281041 -0.0251997308
## 894    No  0.457673081  0.0741500082 -0.9185364846 -0.1683565802
## 895    No  3.373432813  0.5830455387 -0.5132001642  0.4671910550
## 896    No  2.032276355  0.3639354795 -0.6698348771  0.1489419672
## 897   Yes -0.328255504 -0.2670068359 -1.4270396475 -0.3178720101
## 898    No  1.561043715  0.4167998751 -0.4723473183  0.0998332100
## 899    No -2.161418582  0.4322760103  0.2849661847  0.4939584313
## 900   Yes -0.463411359 -0.3063249432 -1.4774471902 -0.3063604629
## 901   Yes -0.150461184 -0.1279512821 -1.1926402596 -0.2084233246
## 902    No  2.213129897  0.4170516907 -0.6029226110  0.2053816336
## 903    No  1.876172251  0.7937595000  0.2039745280  0.0224979983
## 904   Yes -0.187329921 -2.7230819049 -0.3073816726 -0.3079960149
## 905    No -1.456756243  0.0615890460 -0.5701289830  0.0793984076
## 906    No -0.681542804  0.1933733068 -0.4630039086 -0.0453278472
## 907    No -1.976012455  0.5087866646  0.3999477410  0.3979939668
## 908    No  3.200311644  0.6227745042 -0.4002938024  0.4183765271
## 909   Yes -0.680013377 -2.4169255009  0.3836127106 -0.0787852819
## 910    No -0.130524791 -2.5063001911  0.1026708573 -0.1890784008
## 911    No  3.100243750  0.6862269724 -0.2563477811  0.4122658031
## 912    No -1.855501748  0.5620075408  0.4814872277  0.3365554530
## 913    No  0.037563168  1.3240372908  1.6170661759 -0.5987722294
## 914   Yes -1.051463681 -2.5632134146  0.1710627174 -0.0812036198
## 915    No -0.066445476 -2.2419160623  0.6048905810 -0.0957891988
## 916    No  1.562581534  1.0055597726  0.6825312407 -0.0973557726
## 917    No  0.005022434  0.1528149650 -0.6773176279 -0.0743532975
## 918    No  0.291831878 -0.1696096431 -1.3610707347 -0.2268250721
## 919    No -0.337506198  1.1724007756  1.3906571657 -0.4071188898
## 920    No -1.852374807  0.5571447559  0.4715436592  0.3280380091
## 921    No -0.598952410  0.0437140690 -0.7705400923 -0.1093096137
## 922    No  1.581207693  0.7362905590  0.1517700662 -0.0656642316
## 923    No  0.064352107 -2.3162567041  0.4335883448 -0.0897120376
## 924    No  0.131277009  0.2852660077 -0.4429733910 -0.0909327836
## 925   Yes -0.872901977 -2.5967344690  0.0717841867 -0.1533498350
## 926   Yes -0.642461298 -0.0668255623 -0.9764221225 -0.1857608718
## 927    No  2.737072439  0.6283443228 -0.2947048805  0.2684416459
## 928    No  0.289252548  0.1543543944 -0.7294585240 -0.1216225295
## 929    No -0.597043994  0.0479662073 -0.7628414505 -0.0981368143
## 930    No  0.295272782  0.2608884059 -0.5231700293 -0.0843319404
## 931    No -0.201092547  1.3683767765  1.7528268987 -0.6897123799
## 932   Yes -0.720861909 -2.6347547266 -0.0318613290 -0.1872757597
## 933    No -1.586777085  0.4204378584  0.1538713537  0.2311532238
## 934    No -0.757831523 -2.6221003553  0.0002017514 -0.1882438176
## 935   Yes -0.985695182 -0.1532439167 -1.0779073164 -0.1691896969
## 936    No  2.761538392  0.5467136091 -0.4600486051  0.3120785224
## 937    No -1.774157026  0.6036230675  0.5478227255  0.2870793416
## 938    No -1.489469632  0.7130220136  0.7086493709  0.1362408515
## 939    No -1.635417436  0.4686483749  0.2577177091  0.2317432045
## 940    No -0.109841490  0.1290519626 -0.7009395019 -0.0809912570
## 941    No  1.594222937  1.0107239990  0.6855887980 -0.0602593721
## 942    No  2.020968881  0.3909184929 -0.6144771740  0.1313520674
## 943   Yes -1.192758099 -0.1490511654 -1.0299161874 -0.1167109041
## 944    No -2.085159026  0.4485574577  0.3026058761  0.4526589492
## 945    No  0.759792476 -2.2518652834  0.4219295832 -0.0827485991
## 946   Yes  1.097492431 -2.2779460145  0.3041685749 -0.0800448092
## 947    No -1.182006938  0.8669207342  0.9524006320 -0.0348243195
## 948   Yes -1.489737082 -2.2367120583  0.8891760831  0.2377932994
## 949    No -0.966949186 -0.0860966589 -0.9509328610 -0.1412964984
## 950    No -0.773495578  0.3443545937 -0.1509377449  0.0141399834
## 951    No -0.956566434  0.2017682424 -0.3938953196  0.0318539189
## 952    No  0.138955666 -0.0566124143 -1.1113186655 -0.1629634439
## 953   Yes -1.770041822  0.1442182756 -0.3497778328  0.2245053448
## 954    No  0.023024650  1.3093005709  1.5906064351 -0.5741509567
## 955    No -1.448095094  0.0581769120 -0.5784939530  0.0786105063
## 956    No -0.048176408  0.1219639271 -0.7262088718 -0.1172889656
## 957    No  0.382809605  0.1910093508 -0.6766815486 -0.1028473314
## 958    No -1.582744705 -2.0021601059  1.3637825614  0.3465073791
## 959    No -1.705751462  0.6240949082  0.5751382004  0.2489800484
## 960    No -0.959129446 -2.3167671729  0.6315356869  0.0637824387
## 961    No  1.347199679 -1.7037073726  1.3766247038 -0.0413473129
## 962   Yes -1.753514843  0.1333002000 -0.3741433582  0.2130088182
## 963   Yes -0.238289481 -2.7370282588 -0.3245188498 -0.3108040463
## 964   Yes -2.027096882  0.5014570136  0.3954543752  0.4100889834
## 965    No -2.107152008  0.4314334969  0.2731936668  0.4658863165
## 966    No  1.946124762  0.8941914159  0.3863871768  0.0275454990
## 967   Yes -0.876649752 -0.4000471895 -1.5778377486 -0.3625169388
## 968   Yes -1.012279856 -0.3563754911 -1.4669371745 -0.3026104011
## 969    No  1.476775848  0.4027597603 -0.4825157740  0.0700885545
## 970    No  1.098309169  0.7482257604  0.2707576173 -0.0775367534
## 971   Yes -0.401736841 -1.4954627179  2.1312659205 -0.1359564325
## 972    No  1.358726322  0.7169966215  0.1568054559 -0.0091105262
## 973   Yes  3.017669951  0.6392555055 -0.3296746939  0.3092092010
## 974   Yes -1.353561963 -0.1309172298 -0.9637890741 -0.0652071262
## 975    No -0.802218360 -0.0299662256 -0.8748132303 -0.0909577743
## 976   Yes  2.652503815 -1.8666299566  0.7947297018  0.2182984851
## 977    No -0.288206298  0.5369433560  0.1313879884 -0.0659240909
## 978    No -1.640015899  0.6747687248  0.6620959522  0.2075198270
## 979    No -1.068402284  0.9417796786  1.0781613633 -0.1224409210
## 980    No -0.320950109  0.6639010798  0.3864184318 -0.0831255163
## 981   Yes -1.077561421 -0.3132490924 -1.3706933490 -0.2571991210
## 982    No -0.020574489  1.3350075411  1.6504602748 -0.6205426048
## 983   Yes  0.538608819 -2.1313347287  0.7007043727 -0.0566099542
## 984    No -1.390649128  0.3129926870 -0.0930961556  0.1448815820
## 985    No -2.182389936  0.4166242621  0.2581420271  0.5113436842
## 986    No -1.450317558  0.7718565412  0.8168727751  0.0919563219
## 987    No -1.242685039  0.8608802324  0.9524241437 -0.0275034102
## 988    No  1.352736248  0.6303702934 -0.0115286752 -0.0012366713
## 989    No -0.403532037  1.1416522918  1.3432350849 -0.3904123568
## 990    No -1.459926614  0.6427918515  0.5654341352  0.1401006226
## 991    No -1.814797974  0.4688174039  0.2920959682  0.2973085046
## 992    No -1.833118709  0.5752063061  0.5033310024  0.3147407406
## 993   Yes  0.494162723  0.2455181767 -0.5921999404 -0.0990117343
## 994   Yes  0.077984841  0.3799827611 -0.2479698150 -0.0583242240
## 995   Yes -0.544750016 -2.7384125860 -0.2673118528 -0.2810191025
## 996    No -0.124208071  1.3607365835  1.7217598857 -0.6453501650
## 997    No -1.306221341 -0.1201394316 -0.9519172619 -0.0724872845
## 998   Yes -0.632786400 -0.3099770403 -1.4510233731 -0.3111329011
## 999   Yes  0.098675866 -2.1823496189  0.6889572366 -0.1070471347
# Means of scores for all the PC's classified by Survival status
tabmeansPC <- aggregate(teletype_pca[,2:5],by=list(Churn=telecom$Churn),mean)
tabmeansPC
##   Churn        PC1        PC2        PC3         PC4
## 1    No  0.1507995  0.1833937  0.1466455  0.01294252
## 2   Yes -0.4331102 -0.5267238 -0.4211795 -0.03717211
tabmeansPC <- tabmeansPC[rev(order(tabmeansPC$Churn)),]
tabmeansPC
##   Churn        PC1        PC2        PC3         PC4
## 2   Yes -0.4331102 -0.5267238 -0.4211795 -0.03717211
## 1    No  0.1507995  0.1833937  0.1466455  0.01294252
tabfmeans <- t(tabmeansPC[,-1])
tabfmeans
##               2          1
## PC1 -0.43311022 0.15079951
## PC2 -0.52672380 0.18339371
## PC3 -0.42117951 0.14664550
## PC4 -0.03717211 0.01294252
colnames(tabfmeans) <- t(as.vector(tabmeansPC[1]$Churn))
tabfmeans
##             Yes         No
## PC1 -0.43311022 0.15079951
## PC2 -0.52672380 0.18339371
## PC3 -0.42117951 0.14664550
## PC4 -0.03717211 0.01294252
# Standard deviations of scores for all the PC's classified by Survival status
tabsdsPC <- aggregate(teletype_pca[,2:5],by=list(Churn=telecom$Churn),sd)
tabfsds <- t(tabsdsPC[,-1])
colnames(tabfsds) <- t(as.vector(tabsdsPC[1]$Churn))
tabfsds
##            No      Yes
## PC1 1.5284976 1.232376
## PC2 0.9544560 1.078885
## PC3 0.7769390 0.811879
## PC4 0.2510594 0.223820
t.test(PC1~telecom$Churn,data=teletype_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC1 by telecom$Churn
## t = 6.1415, df = 551.12, p-value = 1.566e-09
## alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
## 95 percent confidence interval:
##  0.3971531 0.7706664
## sample estimates:
##  mean in group No mean in group Yes 
##         0.1507995        -0.4331102
t.test(PC2~telecom$Churn,data=teletype_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC2 by telecom$Churn
## t = 9.3721, df = 405.69, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
## 95 percent confidence interval:
##  0.5611678 0.8590672
## sample estimates:
##  mean in group No mean in group Yes 
##         0.1833937        -0.5267238
t.test(PC3~telecom$Churn,data=teletype_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC3 by telecom$Churn
## t = 9.7822, df = 431.77, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
## 95 percent confidence interval:
##  0.4537351 0.6819149
## sample estimates:
##  mean in group No mean in group Yes 
##         0.1466455        -0.4211795
t.test(PC4~telecom$Churn,data=teletype_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC4 by telecom$Churn
## t = 2.999, df = 498.29, p-value = 0.002844
## alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
## 95 percent confidence interval:
##  0.01728354 0.08294572
## sample estimates:
##  mean in group No mean in group Yes 
##        0.01294252       -0.03717211
## F ratio tests
var.test(PC1~telecom$Churn,data=teletype_pca)
## 
##  F test to compare two variances
## 
## data:  PC1 by telecom$Churn
## F = 1.5383, num df = 740, denom df = 257, p-value = 5.458e-05
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  1.251924 1.871549
## sample estimates:
## ratio of variances 
##           1.538306
var.test(PC2~telecom$Churn,data=teletype_pca)
## 
##  F test to compare two variances
## 
## data:  PC2 by telecom$Churn
## F = 0.78264, num df = 740, denom df = 257, p-value = 0.01411
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.6369370 0.9521815
## sample estimates:
## ratio of variances 
##          0.7826386
var.test(PC3~telecom$Churn,data=teletype_pca)
## 
##  F test to compare two variances
## 
## data:  PC3 by telecom$Churn
## F = 0.91578, num df = 740, denom df = 257, p-value = 0.3782
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.745292 1.114165
## sample estimates:
## ratio of variances 
##          0.9157801
var.test(PC4~telecom$Churn,data=teletype_pca)
## 
##  F test to compare two variances
## 
## data:  PC4 by telecom$Churn
## F = 1.2582, num df = 740, denom df = 257, p-value = 0.02905
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  1.023977 1.530782
## sample estimates:
## ratio of variances 
##           1.258215
# Levene's tests (one-sided)
library(car)
## Loading required package: carData
(LTPC1 <- leveneTest(PC1~telecom$Churn,data=teletype_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   1   32.68 1.435e-08 ***
##       997                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(p_PC1_1sided <- LTPC1[[3]][1]/2)
## [1] 7.174053e-09
(LTPC2 <- leveneTest(PC2~telecom$Churn,data=teletype_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value   Pr(>F)   
## group   1  7.3856 0.006689 **
##       997                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(p_PC2_1sided=LTPC2[[3]][1]/2)
## [1] 0.003344413
(LTPC3 <- leveneTest(PC3~telecom$Churn,data=teletype_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   1  0.5699 0.4505
##       997
(p_PC3_1sided <- LTPC3[[3]][1]/2)
## [1] 0.2252423
(LTPC4 <- leveneTest(PC4~telecom$Churn,data=teletype_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   1  2.2864 0.1308
##       997
(p_PC4_1sided <- LTPC4[[3]][1]/2)
## [1] 0.06541319
# Plotting the scores for the first and second components
plot(teletype_pca$PC1, teletype_pca$PC2,pch=ifelse(teletype_pca$Churn == "S",1,16),xlab="PC1", ylab="PC2", main="49 telecom against values for PC1 & PC2")

plot(eigen_telecom, xlab = "Component number", ylab = "Component variance", type = "l", main = "Scree diagram")

plot(log(eigen_telecom), xlab = "Component number",ylab = "log(Component variance)", type="l",main = "Log(eigenvalue) diagram")

print(summary(telecom_pca))
## Importance of components:
##                           PC1    PC2    PC3     PC4
## Standard deviation     1.4795 1.0353 0.8241 0.24519
## Proportion of Variance 0.5472 0.2680 0.1698 0.01503
## Cumulative Proportion  0.5472 0.8152 0.9850 1.00000
diag(cov(telecom_pca$x))
##        PC1        PC2        PC3        PC4 
## 2.18880975 1.07192119 0.67915089 0.06011817
xlim <- range(telecom_pca$x[,1])
telecom_pca$x[,1]
##   [1] -2.015467453 -0.286167867 -1.580345244 -0.287614123 -1.294160708
##   [6] -0.494044929 -0.020111087 -1.733455753  0.688536938  0.800699638
##  [11] -1.254566657 -1.764971394  2.061385552  1.724378831  0.527494462
##  [16]  3.161504599 -0.716173101  2.952410314 -1.254731788 -0.052469384
##  [21] -1.611728253 -1.878281489 -2.175779144  0.775447113  0.410974980
##  [26] -0.507827005  1.525172980 -2.009683010  2.415256278 -0.777763717
##  [31]  2.848230035 -0.641013427 -0.300560723 -2.174952795 -1.519177173
##  [36]  2.827024440 -1.194294975  0.756572527  0.995843188 -0.372576730
##  [41] -1.361697679  1.595061949 -1.686527850  1.605413825 -0.714410979
##  [46]  1.086026186 -1.658263057 -1.134762350  1.167167537  1.311538924
##  [51]  1.264868979 -0.168370241 -0.085154857 -0.614912060  1.580551201
##  [56]  0.176758767  2.346069747  3.020282165 -1.093507929  3.124480162
##  [61]  1.531689184  1.870638938  0.648254123 -0.961557792 -0.545892972
##  [66] -1.169962034  0.875427786  0.182493361 -0.796456606 -0.750675757
##  [71] -1.698149465 -0.700659398  3.032428488 -0.313836135 -1.364614999
##  [76]  2.554954116  0.197136523 -1.322542296  0.217664019 -0.734366957
##  [81] -1.197382016 -1.296764834 -1.008206279  1.361647046 -0.806959336
##  [86] -0.448546799 -0.084717836 -0.797431545 -0.891905672 -1.031259395
##  [91]  0.227101041 -1.032457656  1.987686410  2.806811496  2.903210552
##  [96] -0.708173758  1.543929464 -2.042972026 -0.686131807  0.606006347
## [101] -2.174952795 -2.187348029  0.918938002  0.828260114  3.004049207
## [106] -1.994145410  2.910881473 -1.044980444  1.113535949 -0.182569918
## [111]  1.806754913  0.473311559  1.079176733  0.624327885  0.802448837
## [116] -0.932457938 -0.881816122 -0.368163059 -1.021001971  0.088899116
## [121]  1.959011199 -2.026197593 -1.188782751 -1.447591995 -2.083725783
## [126]  0.539725647  0.209918439 -0.010898566 -2.182389936  1.396133635
## [131] -0.488380801 -0.576201423  0.757771042 -1.922916373 -1.742382162
## [136] -0.791376856 -0.275699196 -0.376504769 -0.576670736 -1.102697315
## [141]  2.637556123 -1.031083507  2.224966267  1.824074123  0.223919674
## [146]  2.412380218 -2.127246954 -1.754341192 -0.242980107 -0.751647226
## [151] -1.073099568 -0.640030879  3.111701929  1.786414072 -2.042218618
## [156] -0.565777248 -0.137336369 -1.581914961 -0.827824399 -1.813761641
## [161] -1.105125107 -0.277685139 -1.315154533  1.019911639 -1.878916383
## [166] -0.242720302 -1.210277456  2.362522478  0.533272788 -1.742987721
## [171]  0.839076685 -0.720591805 -0.540357577  1.661339506 -1.279821564
## [176] -1.130555556 -0.408013662 -0.743385170 -0.028474511 -0.446593399
## [181] -2.013814755 -1.760125634 -0.785685539  0.143094098 -0.627242566
## [186] -2.098928694 -0.938926300 -1.945864424 -1.845639560 -0.013645536
## [191]  0.532751459 -0.763753011 -0.241701043  3.239883891 -0.529586745
## [196]  0.041504261 -1.423797011  2.505245073  3.255949403 -2.165862957
## [201]  0.513172914 -0.591288638  2.940458725 -0.665132866  0.444015173
## [206]  0.294475844  1.216941856 -1.188292177  0.191402077  2.513449429
## [211] -1.714650062 -2.091491554 -0.496532742 -1.390183335  0.214739477
## [216]  0.714439146  0.750808255  0.986205791  1.855475220 -0.869756792
## [221] -1.223800243  0.018466833 -2.174952795 -1.575912620 -1.880644639
## [226] -0.790721995  0.228193786 -1.596508547  0.398788586  1.111447309
## [231]  2.117501542  1.498031583 -1.110615378 -0.109889215 -1.259735971
## [236] -1.569694178 -1.736715414 -0.556239678 -0.172771995 -1.764254088
## [241]  2.350509329  3.159196787  0.536800409  2.494646248 -0.892448846
## [246] -0.896128512  0.189676268 -0.429468453 -1.706412954  1.275306480
## [251]  1.483814874 -1.300333090 -1.602638415  0.317688173 -1.925680891
## [256]  1.147868075  2.752892848  2.138312705 -1.738525078 -0.543376534
## [261] -1.515062327  0.136554351  1.891387507 -0.576583362  1.787988537
## [266]  1.886173788 -0.642898886  0.428243968 -0.555691572 -0.019705730
## [271]  0.045191278  0.734348784 -2.098928694  0.531953653 -1.341993078
## [276] -0.915016951  1.984786439 -0.369501616 -1.096447796 -1.526109774
## [281] -1.406045462 -1.328385636 -2.089012507  0.967514972 -0.061965617
## [286] -0.280762554 -1.087855913 -1.351909265 -0.722508773 -1.449667016
## [291] -0.012310872 -0.156304632 -0.037168857 -0.538131197 -1.874672271
## [296] -2.174126447  1.892157482  1.137964837  0.461889938 -1.292412142
## [301] -0.517387135 -0.534272919 -0.869454569  1.184296677  0.571289095
## [306] -0.589184662  0.321175896 -0.050346927  1.299967751  0.905048451
## [311] -2.190653425 -0.039180670  1.731201079 -0.951062247 -0.988780961
## [316]  2.060995141 -0.199582997  0.522109306  0.414408076  0.687022178
## [321]  1.536586078  1.315341185 -1.768389124 -1.415338168  1.222586093
## [326]  1.805900140 -0.438710303 -1.061712015 -0.787641432 -0.135536917
## [331] -1.198343873 -1.990778442  1.335829067 -1.025166682 -1.132206039
## [336]  1.778571815  1.522412449  2.226159230  0.858588810  2.491325846
## [341] -0.144465070  2.277300407  1.370391266 -0.379837665 -1.018866996
## [346] -1.075427800 -0.969489948 -0.244584145 -0.989634656  2.602197147
## [351] -0.010310742 -1.223173899 -0.516709345 -0.955977575 -0.888255721
## [356] -0.756135568 -0.789894582  2.607862820 -0.942772675  1.163010501
## [361] -2.065476607  1.151186059  0.438417864 -0.854009680 -0.492185858
## [366] -0.708337001 -0.627774818 -2.192306123  2.700440177  3.286207534
## [371] -1.245912508 -1.042774548 -1.164255026  1.985072659  0.925935526
## [376]  0.888440164 -2.089838856  0.483999792  1.848300681 -0.328025642
## [381]  0.767308022 -1.671706299  1.770465319 -1.007321763  1.782055683
## [386] -1.653232760  1.759745750 -0.006995568  1.113139875 -1.781610707
## [391]  0.386039297  0.369844689 -1.499091860 -1.669436800  1.350609046
## [396]  2.158696031  1.314538651  0.173450140 -0.130133918 -1.562150792
## [401] -1.301600987 -1.886748566  2.680816993  1.037622041 -1.634917983
## [406] -0.145573011  2.064404873  0.791862939 -2.179910889 -2.184868983
## [411] -0.832954966 -0.778633681 -0.032724793  1.341582038  0.975572007
## [416] -0.632027926  2.648422726 -0.921588574 -0.144214218 -1.022541469
## [421] -1.984879235 -1.088903843  0.579968278 -0.791065474 -1.513035429
## [426]  0.622222000  2.155542216 -0.659936889 -0.490696660  1.112469866
## [431] -0.485346062  1.550248609 -1.583558920 -1.371043561 -1.017025873
## [436] -0.875376170 -1.164910240  3.408500081  0.638502621 -1.598987594
## [441]  0.211180231  1.941101101  2.308994549 -0.732085263  0.443198603
## [446]  2.403876406 -1.359346405 -0.573228064 -0.591232088  3.021994943
## [451] -0.197906966 -0.209341868  0.848218582  0.066115975 -0.336113247
## [456]  0.427460789  0.415018801  0.148720263 -2.150278386 -1.267621674
## [461] -2.046673375 -0.390588782 -0.686440899 -0.556957327  3.664449559
## [466]  0.522505972  2.716104695  2.469786466 -0.955326849 -1.114668310
## [471] -1.471717864 -1.599813943 -1.025952606 -0.734317916 -1.274232466
## [476] -0.143678059  0.536500814 -0.982752463 -0.726151046 -0.781912460
## [481] -1.896698650 -0.082609785 -0.028423837  3.184114370 -0.796080886
## [486]  2.252905439 -0.154616411  2.340036838 -1.280016908  2.512396435
## [491] -1.494985556 -1.237622292  1.267859891 -2.171647400 -1.058855892
## [496] -0.388707308 -0.211680600 -1.676064236 -0.281294057  1.257730880
## [501]  2.278696143  1.434933438  1.268504013  1.920925370  0.209019199
## [506] -0.768218171 -0.907988452 -0.942389187 -2.180737238  0.222646044
## [511]  2.407741051 -0.871838925  2.166835286  0.518969956  1.275796804
## [516] -0.565077168 -0.950971276  0.104039221 -1.855949878  2.726633388
## [521] -0.374523696  1.472148386 -0.271709891  0.873523356  1.504387949
## [526]  3.657915782  1.897145736 -1.217553028  2.257587627 -1.500482593
## [531] -0.218434082 -1.137368632  3.132456689 -1.104004587 -0.508759846
## [536]  1.681474070 -0.265534027  2.542959902  1.573912241  3.329555277
## [541] -1.149886328 -2.185695331 -0.665396450 -1.323252191  0.290128469
## [546]  0.702260442  2.604507411  2.025966641 -1.779151384  3.202674133
## [551]  3.362025767 -0.631283339 -1.443220224  0.252550667  0.961174074
## [556] -2.179910889  0.263281260 -0.921399911 -1.694017720  2.229702111
## [561] -2.054286986 -1.091137141  2.122587928 -1.199117557  1.673845329
## [566] -0.053270584  1.827997486  0.913308574 -1.502850478 -0.533484371
## [571]  0.544662525 -1.025617080  1.995752636  1.074332370  1.546446407
## [576]  0.657681147 -1.008960174  1.015632917 -2.155730345 -1.882222441
## [581] -1.264316279 -0.650186458 -2.194785170 -2.120650619 -0.850660892
## [586]  0.646164920 -2.066710087  2.864111448  2.481246350  3.258766168
## [591] -0.739914165  1.830504634  0.225588535 -1.755167541 -1.050844002
## [596] -1.011641489 -1.307500380  1.431220027 -0.310959295 -0.618218890
## [601] -2.148285852  1.582172879  1.697947741  1.019238499  2.277235189
## [606]  0.541065110  0.088344264  3.369738816  2.861716043 -1.768292598
## [611] -1.079432495 -0.302328719  1.900456036  0.724000688 -1.214170222
## [616] -1.885499395  2.900554160  1.600556406 -0.945466070 -1.396189849
## [621]  2.039311129  0.730658097 -1.638517480 -2.007603845  0.275487690
## [626] -0.070682533  2.883492436  3.459590282  1.603114530  1.843248199
## [631]  0.124450836  2.464690667 -1.922404657 -0.088247863  2.681607106
## [636]  0.688451585  1.588390422  2.358637105 -0.672257476 -0.101957181
## [641]  0.082126335 -1.028806835  1.524682283 -1.665774215  0.250225114
## [646] -1.753514843  0.733360701 -0.744266292 -0.105608419 -1.269632476
## [651] -1.275885164 -1.218584626 -1.604284883 -1.741017171 -0.509481193
## [656]  2.232972153  0.812972782 -2.153321210 -1.156729662 -2.018932848
## [661] -1.445108950 -2.177431842  1.367403811 -0.579147415 -1.180627555
## [666] -1.313089719 -0.505065310 -1.643976554  1.169102046 -0.701617260
## [671] -0.523295116 -1.268448023 -1.484346965  0.430135923  3.077450325
## [676] -0.691618253 -1.904570742 -0.619702252  0.906755103 -1.186639480
## [681]  1.390674210 -1.360962414  1.516842469 -1.333729588 -1.684101533
## [686] -0.604423912 -1.418194032 -0.389125464  1.183898927 -2.170821051
## [691]  0.074205758 -0.834537702 -1.165519115 -1.342602374 -2.167515655
## [696]  2.317047742 -1.600302648  1.321749700  1.579207336  1.210790517
## [701]  0.439287844  0.234990959 -2.142619673 -1.580489627 -0.082916959
## [706]  0.997861324  0.881378370  0.006018899  0.069042241 -2.185695331
## [711] -0.274007379 -0.370339377 -0.479711592  0.015368512  1.191172140
## [716]  1.230004587  0.358314608 -0.752482592  2.179619376 -2.147970441
## [721] -0.430995578 -0.934586341 -1.685949334  0.894142747 -1.680623950
## [726] -1.429088383 -1.001909455  0.679910616  1.543088643  1.049696523
## [731] -2.060438882 -0.186597645  2.048719231  0.247858324 -0.503075603
## [736]  0.907073946  2.751283546  0.922089225  2.745337154  0.426971904
## [741] -1.140048192 -0.411986845 -0.302329766 -1.643972230  3.428094186
## [746]  3.586307177 -0.944158278 -0.878537118  2.047305030 -0.518047766
## [751]  1.983285330 -1.064460315 -0.963854549  0.298740306 -0.345996608
## [756] -2.124387321 -0.428057904  2.472954157 -2.165036608 -0.029688187
## [761] -1.261342692  1.569625251 -0.354307039 -1.594732604 -0.287494106
## [766] -1.801751759  0.501000967 -0.752287842 -1.880369068 -0.256461578
## [771] -2.179910889 -0.842846817  0.653585961  3.236907612 -1.782117234
## [776] -1.101132029  2.328374615 -1.723759091  1.766798933 -1.626503007
## [781] -0.590954027 -1.646089483  0.311061105  1.953432764  1.157955043
## [786] -0.189852042 -0.182131386  1.658299685  0.844790437  1.718097422
## [791] -1.984661766  0.017621739 -1.577856377 -1.402019743  0.237963047
## [796] -1.514484261 -2.178258191  2.222486439  2.097419072 -0.398429662
## [801] -0.995556301  0.428675364 -0.867509713  1.936363311 -0.919366763
## [806]  3.050031277  1.213514445 -1.359346405  2.205777418  2.847600120
## [811] -0.844588905 -0.992189274 -1.823130668  0.015231636 -1.034653249
## [816]  2.040415272  0.422277993  2.222438148  2.536566506  0.764170916
## [821]  1.626584603 -1.287315744 -0.248379102 -0.301176802 -0.391736998
## [826] -1.690154773  1.888469307 -0.611852042  1.991976537 -0.980644345
## [831]  1.775803697  0.718857287 -0.833687139  2.260440877  1.337255339
## [836] -1.774999915  0.399803256 -0.936380515  2.179479803  3.007587734
## [841] -1.870374160 -1.620610449 -1.023022392 -1.770685763  1.904973786
## [846] -1.591395342  2.562990804  2.448714628  3.439316005  1.325410808
## [851] -2.064585965 -1.270831634 -0.237987106  2.361032923  2.329768106
## [856] -1.669227253  2.122174298  1.525047644 -1.485682414  2.126009898
## [861] -0.215244250 -0.830151303  0.114865431 -1.039427478  0.189592082
## [866] -2.054663910  1.671397530 -1.999511429  2.731246468  1.969118266
## [871] -0.337513664  0.535123171  1.452114263 -1.865223934 -0.025739745
## [876]  0.496305932  1.054255883 -0.411139432 -0.214392747 -1.238466984
## [881] -0.888712772  2.972601376 -0.319042954 -2.177431842 -0.584445282
## [886]  0.945607898  0.730940347  2.332972033  0.440689837  1.744270485
## [891]  0.513182458 -2.102234090  1.657301836  0.457673081  3.373432813
## [896]  2.032276355 -0.328255504  1.561043715 -2.161418582 -0.463411359
## [901] -0.150461184  2.213129897  1.876172251 -0.187329921 -1.456756243
## [906] -0.681542804 -1.976012455  3.200311644 -0.680013377 -0.130524791
## [911]  3.100243750 -1.855501748  0.037563168 -1.051463681 -0.066445476
## [916]  1.562581534  0.005022434  0.291831878 -0.337506198 -1.852374807
## [921] -0.598952410  1.581207693  0.064352107  0.131277009 -0.872901977
## [926] -0.642461298  2.737072439  0.289252548 -0.597043994  0.295272782
## [931] -0.201092547 -0.720861909 -1.586777085 -0.757831523 -0.985695182
## [936]  2.761538392 -1.774157026 -1.489469632 -1.635417436 -0.109841490
## [941]  1.594222937  2.020968881 -1.192758099 -2.085159026  0.759792476
## [946]  1.097492431 -1.182006938 -1.489737082 -0.966949186 -0.773495578
## [951] -0.956566434  0.138955666 -1.770041822  0.023024650 -1.448095094
## [956] -0.048176408  0.382809605 -1.582744705 -1.705751462 -0.959129446
## [961]  1.347199679 -1.753514843 -0.238289481 -2.027096882 -2.107152008
## [966]  1.946124762 -0.876649752 -1.012279856  1.476775848  1.098309169
## [971] -0.401736841  1.358726322  3.017669951 -1.353561963 -0.802218360
## [976]  2.652503815 -0.288206298 -1.640015899 -1.068402284 -0.320950109
## [981] -1.077561421 -0.020574489  0.538608819 -1.390649128 -2.182389936
## [986] -1.450317558 -1.242685039  1.352736248 -0.403532037 -1.459926614
## [991] -1.814797974 -1.833118709  0.494162723  0.077984841 -0.544750016
## [996] -0.124208071 -1.306221341 -0.632786400  0.098675866
telecom_pca$x
##                  PC1           PC2           PC3           PC4
##    [1,] -2.015467453  0.3063516984  0.0120502201  0.3952287653
##    [2,] -0.286167867  0.5013439720  0.0615892254 -0.0753083935
##    [3,] -1.580345244  0.0591421382 -0.5512321189  0.1140939064
##    [4,] -0.287614123  0.7983943370  0.6445959152 -0.1696250516
##    [5,] -1.294160708 -0.1237314581 -0.9613547414 -0.0709556042
##    [6,] -0.494044929 -0.3379468993 -1.5326506543 -0.3329395336
##    [7,] -0.020111087  0.0003749667 -0.9685190929 -0.1613687025
##    [8,] -1.733455753  0.4319562059  0.2043525014  0.2789892675
##    [9,]  0.688536938 -0.0510378498 -1.2097481522 -0.1275878542
##   [10,]  0.800699638  0.9284002528  0.6841006823 -0.1865781716
##   [11,] -1.254566657  0.2600970846 -0.2216823424  0.0644229830
##   [12,] -1.764971394  0.6268866250  0.5916904672  0.2774977466
##   [13,]  2.061385552  0.4838318990 -0.4400631575  0.0956542225
##   [14,]  1.724378831  0.3072806955 -0.7177116306  0.0522494039
##   [15,]  0.527494462 -0.1112877649 -1.2945144595 -0.1843081668
##   [16,]  3.161504599  0.5720136417 -0.4917171390  0.4115436863
##   [17,] -0.716173101  1.0901673293  1.3032764892 -0.3397861962
##   [18,]  2.952410314  0.6478858084 -0.2992142283  0.2764189167
##   [19,] -1.254731788  0.1623572800 -0.4124580865  0.0517707540
##   [20,] -0.052469384 -0.0261847489 -1.0136995538 -0.1778530396
##   [21,] -1.611728253 -2.1930906514  0.9970540300  0.3085286329
##   [22,] -1.878281489  0.5620845058  0.4865222098  0.3184532575
##   [23,] -2.175779144  0.4122570318  0.2483958170  0.5067450736
##   [24,]  0.775447113  0.8376438460  0.5105457067 -0.1338228327
##   [25,]  0.410974980  0.7056174597  0.3236927933 -0.0983047154
##   [26,] -0.507827005  0.4543022412  0.0135374770 -0.0810125188
##   [27,]  1.525172980  0.3179618635 -0.6575552351  0.0560433902
##   [28,] -2.009683010  0.3025303719  0.0035222862  0.3912049809
##   [29,]  2.415256278  0.7991045643  0.1058810951  0.1186320774
##   [30,] -0.777763717  0.1696083634 -0.4906300199 -0.0370124895
##   [31,]  2.848230035 -1.6564358066  1.1668468777  0.2246353601
##   [32,] -0.641013427 -2.7867310927 -0.3417486462 -0.3284125213
##   [33,] -0.300560723  0.3117621795 -0.3071772993 -0.0288213652
##   [34,] -2.174952795  0.4117111280  0.2471775407  0.5061702472
##   [35,] -1.519177173 -2.2542318748  0.8606070875  0.2441480838
##   [36,]  2.827024440  0.7296306943 -0.1149545366  0.2914726586
##   [37,] -1.194294975 -0.0682028508 -0.8724635335 -0.0740242687
##   [38,]  0.756572527  0.5250342636 -0.0992482896 -0.0213891894
##   [39,]  0.995843188  0.0282164677 -1.1156929653 -0.1195278411
##   [40,] -0.372576730 -0.2687303412 -1.4222942619 -0.2876389053
##   [41,] -1.361697679  0.2221115384 -0.2755626470  0.1014410539
##   [42,]  1.595061949  0.9430453465  0.5533983805 -0.0736439939
##   [43,] -1.686527850  0.6235121074  0.5699017654  0.2630821071
##   [44,]  1.605413825  0.7377433815  0.1493460653 -0.0429488503
##   [45,] -0.714410979 -0.0113787300 -0.8552542721 -0.1177632548
##   [46,]  1.086026186  0.4712426940 -0.2680799863 -0.0881353262
##   [47,] -1.658263057  0.1090959181 -0.4392579796  0.1648477748
##   [48,] -1.134762350 -0.2330839393 -1.2040775207 -0.1910210350
##   [49,]  1.167167537  0.5738663650 -0.0853678670  0.0005600547
##   [50,]  1.311538924  0.9603726853  0.6458001905 -0.1921306285
##   [51,]  1.264868979 -2.0625593971  0.6907915360 -0.0149786634
##   [52,] -0.168370241 -0.2188635628 -1.3651104889 -0.2895317085
##   [53,] -0.085154857 -2.1475877081  0.7917325457 -0.0363147592
##   [54,] -0.614912060 -2.5298658743  0.1513254615 -0.1432407568
##   [55,]  1.580551201 -1.6543390313  1.4266039081 -0.0209865789
##   [56,]  0.176758767 -2.5201212919  0.0148139888 -0.1829799378
##   [57,]  2.346069747  0.5803719891 -0.3096712143  0.1944602172
##   [58,]  3.020282165 -1.8392739689  0.7738886278  0.2966004227
##   [59,] -1.093507929  0.8111109188  0.8255104785 -0.0206660269
##   [60,]  3.124480162  0.6710979411 -0.2903972792  0.3974064804
##   [61,]  1.531689184  0.3036294823 -0.6862831312  0.0287731236
##   [62,]  1.870638938  0.6140627227 -0.1478439577  0.0985073036
##   [63,]  0.648254123  1.1866591365  1.2240615826 -0.4203028134
##   [64,] -0.961557792  0.2894863205 -0.2211229268  0.0176449277
##   [65,] -0.545892972 -0.2663085838 -1.3834428268 -0.2818011253
##   [66,] -1.169962034 -0.1577506121 -1.0513963954 -0.1181469042
##   [67,]  0.875427786  0.4968895086 -0.1769417601 -0.0595475609
##   [68,]  0.182493361  0.2447198211 -0.5327578437 -0.0720772747
##   [69,] -0.796456606  1.0666790373  1.2727579581 -0.3180565883
##   [70,] -0.750675757 -0.0930231842 -1.0075922102 -0.1228832013
##   [71,] -1.698149465  0.0967246467 -0.4557678685  0.1744954540
##   [72,] -0.700659398  1.0956912830  1.3104807748 -0.3148137478
##   [73,]  3.032428488 -1.8980463204  0.6562547371  0.3124827647
##   [74,] -0.313836135  1.1931437520  1.4280892831 -0.4804957131
##   [75,] -1.364614999 -0.0421342756 -0.7891642665 -0.0121639001
##   [76,]  2.554954116 -2.0261799036  0.5025524213  0.1964623697
##   [77,]  0.197136523  0.6995581852  0.3535888524 -0.0745083433
##   [78,] -1.322542296  0.1413066356 -0.4410049403  0.0890350495
##   [79,]  0.217664019 -2.1274182062  0.7726062771 -0.0961275654
##   [80,] -0.734366957  0.9524571386  1.0342366316 -0.1787310509
##   [81,] -1.197382016 -0.2340930443 -1.1940432895 -0.1738493029
##   [82,] -1.296764834  0.2274303565 -0.2778753067  0.0958974213
##   [83,] -1.008206279 -0.0953456690 -0.9611949560 -0.1256688903
##   [84,]  1.361647046  0.1888972503 -0.8759652645 -0.0193031968
##   [85,] -0.806959336  1.0558336138  1.2528522851 -0.2813738779
##   [86,] -0.448546799 -0.3174794868 -1.5019068907 -0.3197269722
##   [87,] -0.084717836  0.4703519543 -0.0392572419 -0.0536551817
##   [88,] -0.797431545  1.0412029346  1.2214304455 -0.2372032057
##   [89,] -0.891905672  1.0183499064  1.1951683772 -0.2254186136
##   [90,] -1.031259395  0.6564413875  0.5098277540  0.0270728460
##   [91,]  0.227101041  0.2038970410 -0.6216515858 -0.0591512269
##   [92,] -1.032457656 -2.5757692015  0.1430423631 -0.0944246254
##   [93,]  1.987686410  0.7651075091  0.1239313568  0.1167016622
##   [94,]  2.806811496  0.5133466217 -0.5333892179  0.2727432484
##   [95,]  2.903210552  0.7271987352 -0.1359404036  0.3470841182
##   [96,] -0.708173758 -0.0563325608 -0.9437915035 -0.1449897800
##   [97,]  1.543929464  0.9763055519  0.6292716107 -0.1089530202
##   [98,] -2.042972026  0.4566118480  0.3103904728  0.4350686525
##   [99,] -0.686131807  1.0897963793  1.2961226931 -0.3165244945
##  [100,]  0.606006347 -2.4340735414  0.0971351316 -0.1313806771
##  [101,] -2.174952795  0.4117111280  0.2471775407  0.5061702472
##  [102,] -2.187348029  0.4198996847  0.2654516848  0.5147926422
##  [103,]  0.918938002  0.2052854759 -0.7556317176 -0.0585346918
##  [104,]  0.828260114 -1.3164589611  2.2411930707 -0.2766375917
##  [105,]  3.004049207  0.5833891941 -0.4377168502  0.3807084725
##  [106,] -1.994145410  0.4204330920  0.2309257221  0.3922088180
##  [107,]  2.910881473  0.6851658542 -0.2177366027  0.2579300175
##  [108,] -1.044980444  0.7303122424  0.6580689327 -0.0255384601
##  [109,]  1.113535949  0.2883479476 -0.6316082014 -0.0625671835
##  [110,] -0.182569918  1.3696846049  1.7513460190 -0.6718857738
##  [111,]  1.806754913  0.4673260818 -0.4213335735  0.0630347745
##  [112,]  0.473311559  0.7644325971  0.4269041449 -0.1240317493
##  [113,]  1.079176733  0.3192866846 -0.5652398537 -0.0199814513
##  [114,]  0.624327885 -2.0273332320  0.8865403656 -0.0308186348
##  [115,]  0.802448837  0.9679188640  0.7620389149 -0.2349692600
##  [116,] -0.932457938 -0.3170301421 -1.4060826680 -0.2887548140
##  [117,] -0.881816122  0.7789851697  0.7217833082 -0.0630673719
##  [118,] -0.368163059 -0.3092994349 -1.5020791769 -0.3063862092
##  [119,] -1.021001971  0.9439411638  1.0735904064 -0.1492104927
##  [120,]  0.088899116  0.1143871675 -0.7671133245 -0.1638923674
##  [121,]  1.959011199  0.4578647766 -0.4705680350  0.0940391395
##  [122,] -2.026197593  0.4729935049  0.3395070540  0.4159711657
##  [123,] -1.188782751 -0.1484856985 -1.0296909860 -0.1122392064
##  [124,] -1.447591995  0.1665799333 -0.3674576470  0.1157125107
##  [125,] -2.083725783  0.4441172020  0.2938314490  0.4437406886
##  [126,]  0.539725647  0.1848646509 -0.7205916833 -0.0605840051
##  [127,]  0.209918439 -2.2003618683  0.6307395561 -0.0586370421
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##  [438,]  3.408500081  0.6245864092 -0.4400342944  0.5198183099
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##  [449,] -0.591232088 -0.2867533777 -1.4141775823 -0.2948348188
##  [450,]  3.021994943  0.6830579553 -0.2455994728  0.3422993016
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##  [562,] -1.091137141 -0.0348263727 -0.8279982987 -0.0549800251
##  [563,]  2.122587928  0.5131676009 -0.3957788717  0.1415753188
##  [564,] -1.199117557  0.0214663442 -0.6974857740 -0.0139726728
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##  [566,] -0.053270584 -0.2396443997 -1.4294351101 -0.2443047012
##  [567,]  1.827997486  0.9284739694  0.4771071436  0.0105042169
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##  [571,]  0.544662525 -1.7209054063  1.5027342681 -0.0969280354
##  [572,] -1.025617080  0.0755901997 -0.6255953298 -0.0308487862
##  [573,]  1.995752636  0.4564565383 -0.4811375369  0.1203244920
##  [574,]  1.074332370 -2.5032740987 -0.1308792095 -0.1216458624
##  [575,]  1.546446407  0.6947299827  0.0770220702 -0.0483896148
##  [576,]  0.657681147  0.0621928273 -0.9827770719 -0.1046992050
##  [577,] -1.008960174 -0.0150494268 -0.8049630351 -0.0836058633
##  [578,]  1.015632917 -2.2298798083  0.4133892419 -0.0367334917
##  [579,] -2.155730345  0.4310947850  0.2814931548  0.4958438319
##  [580,] -1.882222441  0.5721390745  0.5065403730  0.3380898602
##  [581,] -1.264316279 -0.1898748380 -1.0953629115 -0.1272883700
##  [582,] -0.650186458 -2.6857386845 -0.1442457443 -0.2461762482
##  [583,] -2.194785170  0.4248128188  0.2764161712  0.5199660792
##  [584,] -2.120650619  0.4407919984  0.2939354822  0.4762762714
##  [585,] -0.850660892 -2.6958680332 -0.1249784168 -0.2208864184
##  [586,]  0.646164920  0.7186945199  0.3025968154 -0.0890576214
##  [587,] -2.066710087  0.4658407485  0.3330824057  0.4369493931
##  [588,]  2.864111448  0.7448577721 -0.0938772496  0.3557554938
##  [589,]  2.481246350  0.7971493956  0.0865134335  0.2368451888
##  [590,]  3.258766168  0.6318159490 -0.3941178360  0.4160761643
##  [591,] -0.739914165  0.9742884937  1.0785348542 -0.2033806311
##  [592,]  1.830504634  0.7213294677  0.0697458803  0.1004284995
##  [593,]  0.225588535  0.1738268073 -0.6786662511 -0.1285483559
##  [594,] -1.755167541  0.1343920076 -0.3717068057  0.2141584709
##  [595,] -1.050844002  0.1244773357 -0.5254829700 -0.0099394510
##  [596,] -1.011641489  0.2576882687 -0.2739673362  0.0447623361
##  [597,] -1.307500380 -0.0385909949 -0.7931849131 -0.0280062689
##  [598,]  1.431220027  0.4614239571 -0.3579188942  0.0271557634
##  [599,] -0.310959295  1.2726927788  1.5835961660 -0.5069150169
##  [600,] -0.618218890  0.0522521294 -0.7501250237 -0.1054076855
##  [601,] -2.148285852  0.4281730361  0.2743243504  0.4951917175
##  [602,]  1.582172879  0.8367979518  0.3476514870 -0.0460946531
##  [603,]  1.697947741  0.2097854109 -0.9023847965  0.0190778336
##  [604,]  1.019238499 -0.0296192361 -1.2339546952 -0.0924963473
##  [605,]  2.277235189  0.8272401224  0.1891486453  0.0716913492
##  [606,]  0.541065110  0.3373005640 -0.4228132369 -0.0623694426
##  [607,]  0.088344264  0.8343382509  0.6413331292 -0.2046892586
##  [608,]  3.369738816  0.6124384117 -0.4548809847  0.4611739286
##  [609,]  2.861716043 -1.8287198570  0.8265609058  0.2630114464
##  [610,] -1.768292598  0.4149956299  0.1780079596  0.2822821784
##  [611,] -1.079432495  0.0479054609 -0.6697955195  0.0026014287
##  [612,] -0.302328719  1.2812815617  1.5996005170 -0.5502166827
##  [613,]  1.900456036 -2.2222074274  0.2514583020  0.0632679446
##  [614,]  0.724000688  0.6281323774  0.1102487099 -0.0925537933
##  [615,] -1.214170222  0.2991419913 -0.1529405607  0.0459653493
##  [616,] -1.885499395  0.4513362250  0.2709758768  0.3403470408
##  [617,]  2.900554160 -1.7819984831  0.9087960118  0.3304108207
##  [618,]  1.600556406  0.5787728150 -0.1616169279  0.0108979220
##  [619,] -0.945466070 -0.1315356478 -1.0436667744 -0.1573909752
##  [620,] -1.396189849 -2.0105968858  1.3120994846  0.2679512518
##  [621,]  2.039311129  0.6282299871 -0.1540661748  0.1265587455
##  [622,]  0.730658097  0.3292327082 -0.4759236650 -0.0679504223
##  [623,] -1.638517480  0.6723280793  0.6571204828  0.2031879319
##  [624,] -2.007603845  0.4942780724  0.3775823180  0.4094506014
##  [625,]  0.275487690 -0.0098006453 -1.0469171901 -0.1563791411
##  [626,] -0.070682533  0.0668872982 -0.8293596549 -0.1208291101
##  [627,]  2.883492436 -1.8076460256  0.8635513765  0.2585665528
##  [628,]  3.459590282 -1.7631369929  0.8336737304  0.4035000740
##  [629,]  1.603114530 -1.9556835434  0.8308775158  0.0805359074
##  [630,]  1.843248199 -2.2523018254  0.2048701277  0.0188314321
##  [631,]  0.124450836  0.6978439314  0.3659173970 -0.1367127807
##  [632,]  2.464690667  0.8114438502  0.1188022352  0.1862734946
##  [633,] -1.922404657  0.5298074069  0.4314852843  0.3492667075
##  [634,] -0.088247863  0.6174510895  0.2493897309 -0.0714485531
##  [635,]  2.681607106  0.5691796817 -0.4000571567  0.2988891466
##  [636,]  0.688451585  0.0479932180 -1.0164564209 -0.1122086828
##  [637,]  1.588390422  0.9008362273  0.4713860351 -0.0353028724
##  [638,]  2.358637105 -1.9751545714  0.6419766979  0.1546515517
##  [639,] -0.672257476 -0.1535209188 -1.1397794143 -0.1971437234
##  [640,] -0.101957181  1.2641317404  1.5268592720 -0.5677429452
##  [641,]  0.082126335  0.6485098439  0.2764906041 -0.0734315177
##  [642,] -1.028806835 -0.3454574155 -1.4425716491 -0.2911138745
##  [643,]  1.524682283 -1.9641862252  0.8314947243 -0.0016717424
##  [644,] -1.665774215  0.5480510351  0.4185980847  0.2480289767
##  [645,]  0.250225114 -2.4790261952  0.0803688095 -0.1702560569
##  [646,] -1.753514843  0.1333002000 -0.3741433582  0.2130088182
##  [647,]  0.733360701  0.6274734379  0.1069836842 -0.0865381702
##  [648,] -0.744266292 -2.7218045559 -0.1957872462 -0.2640351449
##  [649,] -0.105608419 -2.1664830361  0.7586122782 -0.0258688176
##  [650,] -1.269632476 -0.0956317315 -0.9115574955 -0.0572615668
##  [651,] -1.275885164 -0.1822321851 -1.0783070437 -0.1192408014
##  [652,] -1.218584626  0.8670253718  0.9604492332 -0.0639341788
##  [653,] -1.604284883  0.5814714629  0.4720886173  0.2337412753
##  [654,] -1.741017171 -1.8806422082  1.6309401747  0.4253599029
##  [655,] -0.509481193 -0.2610660198 -1.3797806589 -0.3104007714
##  [656,]  2.232972153  0.7543464360  0.0537344779  0.1496974528
##  [657,]  0.812972782  0.4706296311 -0.2165710240 -0.0297982459
##  [658,] -2.153321210  0.4287836828  0.2765692771  0.4925363620
##  [659,] -1.156729662  0.8912095581  0.9962492396 -0.0988715058
##  [660,] -2.018932848  0.4082192097  0.2114759164  0.4143276257
##  [661,] -1.445108950  0.2673032317 -0.1714902402  0.1369894646
##  [662,] -2.177431842  0.4133488394  0.2508323695  0.5078947262
##  [663,]  1.367403811  0.8592609603  0.4350925529 -0.0977733814
##  [664,] -0.579147415  1.1716749926  1.4366894521 -0.3935357362
##  [665,] -1.180627555 -0.1519698011 -1.0380846180 -0.1135962329
##  [666,] -1.313089719 -0.1124916092 -0.9358602014 -0.0606566696
##  [667,] -0.505065310  0.9654233043  1.0156716335 -0.2441607788
##  [668,] -1.643976554  0.1775991819 -0.3087408866  0.1922377337
##  [669,]  1.169102046  1.0337211608  0.8177081552 -0.2097959811
##  [670,] -0.701617260  1.1122044242  1.3436531849 -0.3478401265
##  [671,] -0.523295116  1.0619366735  1.2095349510 -0.3187492060
##  [672,] -1.268448023 -0.1871453191 -1.0892715301 -0.1244142384
##  [673,] -1.484346965  0.6446257899  0.5741714432  0.1246660278
##  [674,]  0.430135923 -1.5517783514  1.8572033882 -0.1538286827
##  [675,]  3.077450325 -1.8657046214  0.7097431120  0.3522378759
##  [676,] -0.691618253  1.0045053521  1.1287478095 -0.2355177432
##  [677,] -1.904570742  0.2671231959 -0.0850704256  0.3255529069
##  [678,] -0.619702252 -0.5127103294 -1.8463272616 -0.4815243489
##  [679,]  0.906755103  0.4494703300 -0.2770429071 -0.0025327888
##  [680,] -1.186639480 -0.2411897934 -1.2098808811 -0.1813220452
##  [681,]  1.390674210  0.7687721536  0.2516354903 -0.0054802042
##  [682,] -1.360962414 -0.0402878268 -0.7864271725 -0.0050465637
##  [683,]  1.516842469 -2.2339028159  0.3055597089  0.0077711199
##  [684,] -1.333729588 -0.1440189205 -0.9930277046 -0.0790029582
##  [685,] -1.684101533  0.0874442824 -0.4764785651  0.1647234063
##  [686,] -0.604423912  1.0442991624  1.1903543312 -0.2844312734
##  [687,] -1.418194032 -2.2835919274  0.7844313479  0.1888948386
##  [688,] -0.389125464  1.0112963117  1.0827018384 -0.2562266775
##  [689,]  1.183898927  0.5184632244 -0.1960822022 -0.0419403422
##  [690,] -2.170821051  0.4089816091  0.2410861593  0.5032961156
##  [691,]  0.074205758  0.2817288957 -0.4389502877 -0.0750416327
##  [692,] -0.834537702  1.0279002426  1.2025478794 -0.2274368430
##  [693,] -1.165519115 -0.1544648505 -1.0460843523 -0.1071318536
##  [694,] -1.342602374 -1.6983571966  1.9137392396  0.1825298350
##  [695,] -2.167515655  0.4067979940  0.2362130542  0.5009968103
##  [696,]  2.317047742  0.8528065875  0.2293566606  0.1616052911
##  [697,] -1.600302648  0.1147498462 -0.4394354471  0.1544698503
##  [698,]  1.321749700 -1.9467372493  0.9053559759  0.0144780602
##  [699,]  1.579207336  0.9953192003  0.6594364020 -0.1072367869
##  [700,]  1.210790517  0.9292660418  0.6036672542 -0.1343938736
##  [701,]  0.439287844  0.2662407856 -0.5409097678 -0.0960510437
##  [702,]  0.234990959  0.1578514027 -0.7126253697 -0.0875274048
##  [703,] -2.142619673  0.4210176552  0.2594642744  0.4835131502
##  [704,] -1.580489627  0.1388616329 -0.3962307580  0.1553381962
##  [705,] -0.082916959  0.1422332785 -0.6801035426 -0.0992017910
##  [706,]  0.997861324  0.9387218314  0.6659107778 -0.2140900186
##  [707,]  0.881378370 -2.4578046481 -0.0042496765 -0.1036552435
##  [708,]  0.006018899  0.2526633607 -0.4826995236 -0.0562528850
##  [709,]  0.069042241  0.1979371552 -0.6005777808 -0.1297783035
##  [710,] -2.185695331  0.4188078772  0.2630151322  0.5136429896
##  [711,] -0.274007379  0.0530352650 -0.8165792443 -0.1062673391
##  [712,] -0.370339377  1.1417296028  1.3362598121 -0.3636058185
##  [713,] -0.479711592 -0.0986783197 -1.0706053234 -0.1971095322
##  [714,]  0.015368512  1.3182264624  1.6107485063 -0.6297554425
##  [715,]  1.191172140  0.3964440509 -0.4377088509  0.0357245498
##  [716,]  1.230004587  1.0457646056  0.8290831544 -0.2033252725
##  [717,]  0.358314608  0.1934961176 -0.6666833808 -0.1168615425
##  [718,] -0.752482592  0.4477768830  0.0476788331 -0.0132972179
##  [719,]  2.179619376 -1.5672928219  1.4758666604  0.0994265889
##  [720,] -2.147970441  0.4249006690  0.2680167757  0.4880247561
##  [721,] -0.430995578  1.2162221541  1.4957581127 -0.4524645966
##  [722,] -0.934586341 -0.2562325912 -1.2882156388 -0.2223063940
##  [723,] -1.685949334  0.1662580307 -0.3228387904  0.2025472441
##  [724,]  0.894142747 -2.2652004934  0.3691505784 -0.0748946393
##  [725,] -1.680623950 -1.8839304789  1.6131892857  0.3966576355
##  [726,] -1.429088383  0.6339094568  0.5418793347  0.1447022075
##  [727,] -1.001909455 -0.1887858413 -1.1436797314 -0.1930882774
##  [728,]  0.679910616 -2.2865750335  0.3699273006 -0.0861411573
##  [729,]  1.543088643  0.8225504448  0.3273917753 -0.0400576963
##  [730,]  1.049696523  0.3921795666 -0.4169607059 -0.0177531697
##  [731,] -2.060438882  0.4634155536  0.3271122236  0.4364818479
##  [732,] -0.186597645  0.1852052282 -0.5759142990 -0.0849492207
##  [733,]  2.048719231  0.8955791003  0.3684967892  0.0433048950
##  [734,]  0.247858324  0.0713168642 -0.8833521309 -0.1340167184
##  [735,] -0.503075603  0.5360450217  0.1713463585 -0.0312524707
##  [736,]  0.907073946 -0.0762188964 -1.3017017490 -0.1487501722
##  [737,]  2.751283546  0.6855582725 -0.1856985633  0.2701728350
##  [738,]  0.922089225 -1.9760377019  0.9278518384 -0.0241116165
##  [739,]  2.745337154 -1.5754721202  1.3447902545  0.2559643959
##  [740,]  0.426971904  0.6175377408  0.1493480543 -0.1457867757
##  [741,] -1.140048192 -0.2311820295 -1.1993166068 -0.1909494481
##  [742,] -0.411986845 -0.2929758992 -1.4615487622 -0.3045337759
##  [743,] -0.302329766  1.1874193162  1.4132256794 -0.4145428661
##  [744,] -1.643972230  0.2081815628 -0.2489471107  0.1918850386
##  [745,]  3.428094186 -1.7563385144  0.8533959977  0.3936454341
##  [746,]  3.586307177 -1.7888998191  0.7573563345  0.4467513047
##  [747,] -0.944158278 -2.5491503654  0.1778102546 -0.1026244725
##  [748,] -0.878537118  1.0482427045  1.2522583356 -0.2863135505
##  [749,]  2.047305030  0.6652564041 -0.0836990854  0.1472279869
##  [750,] -0.518047766  0.4062174657 -0.0803960985  0.0108591034
##  [751,]  1.983285330  0.8529727801  0.2983366483  0.0335989639
##  [752,] -1.064460315 -0.0529255034 -0.8682349912 -0.0746159835
##  [753,] -0.963854549 -0.3374820463 -1.4398228535 -0.2906182365
##  [754,]  0.298740306 -2.5252009458 -0.0180899107 -0.2360314581
##  [755,] -0.345996608  1.2863486833  1.6186332586 -0.5737628477
##  [756,] -2.124387321  0.4422508166  0.2975190655  0.4765860679
##  [757,] -0.428057904 -0.0806525520 -1.0458382932 -0.1844946018
##  [758,]  2.472954157  0.8059848124  0.1066194725  0.1805252313
##  [759,] -2.165036608  0.4051602827  0.2325582254  0.4992723313
##  [760,] -0.029688187 -0.0029776516 -0.9728568960 -0.1766546209
##  [761,] -1.261342692 -0.1044042613 -0.9300642112 -0.0705020059
##  [762,]  1.569625251  0.9893120871  0.6500379624 -0.1285457153
##  [763,] -0.354307039  1.2731613139  1.5937914242 -0.5406315179
##  [764,] -1.594732604  0.3807631152  0.0784460847  0.2045097546
##  [765,] -0.287494106  0.0983480240 -0.7243230568 -0.1537444560
##  [766,] -1.801751759  0.5837119553  0.5142979145  0.2894924882
##  [767,]  0.501000967  0.4492214140 -0.1963638048 -0.0498388712
##  [768,] -0.752287842  0.1719052450 -0.4917170020 -0.0113644777
##  [769,] -1.880369068  0.5438112780  0.4506471001  0.3450452499
##  [770,] -0.256461578 -0.1550976312 -1.2246156388 -0.2156215353
##  [771,] -2.179910889  0.4149865507  0.2544871983  0.5096192052
##  [772,] -0.842846817 -0.2729751119 -1.3383481659 -0.2563660230
##  [773,]  0.653585961  0.1101683639 -0.8874586815 -0.1386034802
##  [774,]  3.236907612  0.6452928753 -0.3637288991  0.4290971829
##  [775,] -1.782117234  0.2195868746 -0.2005127124  0.2463115318
##  [776,] -1.101132029 -0.2462133028 -1.2363297703 -0.1938092032
##  [777,]  2.328374615  0.4429224276 -0.5738844398  0.1474032978
##  [778,] -1.723759091  0.1515283635 -0.3442913921  0.2085134569
##  [779,]  1.766798933  0.9217592201  0.4774355433 -0.0538223436
##  [780,] -1.626503007  0.2007147476 -0.2669338159  0.1889701559
##  [781,] -0.590954027  0.4217214443 -0.0351877482 -0.0124803322
##  [782,] -1.646089483  0.0623327085 -0.5325192736  0.1382813951
##  [783,]  0.311061105  1.0744357382  1.0691161408 -0.3179951819
##  [784,]  1.953432764 -2.1986226649  0.2880204495  0.0198482236
##  [785,]  1.157955043  1.0840108551  0.9189525063 -0.2441107897
##  [786,] -0.189852042  0.4632954375 -0.0316314372 -0.0843062233
##  [787,] -0.182131386  0.1380091505 -0.6683471199 -0.1186808761
##  [788,]  1.658299685  0.9647724373  0.5842163662 -0.1130433018
##  [789,]  0.844790437  0.8668738805  0.5543604557 -0.1513107229
##  [790,]  1.718097422  0.8396726159  0.3269232479 -0.0699231335
##  [791,] -1.984661766  0.5088832504  0.4019879391  0.3912734316
##  [792,]  0.017621739  0.4025784924 -0.1919301933 -0.0555195966
##  [793,] -1.577856377  0.2143321025 -0.2499276651  0.1891764723
##  [794,] -1.402019743 -0.0528256539 -0.8030033935  0.0032839973
##  [795,]  0.237963047  0.2194376944 -0.5928699404 -0.0848993476
##  [796,] -1.514484261  0.6123477494  0.5161315444  0.1666985309
##  [797,] -2.178258191  0.4138947432  0.2520506458  0.5084695526
##  [798,]  2.222486439  0.5919214960 -0.2626077093  0.1911957956
##  [799,]  2.097419072 -1.4979183454  1.6287497737  0.0513784138
##  [800,] -0.398429662 -0.2903840332 -1.4595156664 -0.2877795344
##  [801,] -0.995556301  0.8870605562  0.9567099166 -0.1183682895
##  [802,]  0.428675364  0.6190437099  0.1503752716 -0.0713042397
##  [803,] -0.867509713 -0.2200270682 -1.2306133233 -0.2257961353
##  [804,]  1.936363311  0.9094523048  0.4190608681 -0.0153836574
##  [805,] -0.919366763  0.2848725717 -0.2389742433  0.0410341867
##  [806,]  3.050031277  0.6372242254 -0.3404923268  0.3305675558
##  [807,]  1.213514445  0.1822957316 -0.8597238709 -0.0137200857
##  [808,] -1.359346405 -0.1270959033 -0.9552611401 -0.0611833419
##  [809,]  2.205777418  0.4658907919 -0.5052585676  0.1708220713
##  [810,]  2.847600120  0.6594518806 -0.2561475903  0.2882541588
##  [811,] -0.844588905  0.9173491609  0.9865066702 -0.1376680767
##  [812,] -0.992189274  0.7532071641  0.6933554800 -0.0706712578
##  [813,] -1.823130668 -1.9256843203  1.5582356836  0.4664494989
##  [814,]  0.015231636  0.0931668542 -0.7947268842 -0.1317119758
##  [815,] -1.034653249 -0.2924866378 -1.3388312167 -0.2453955409
##  [816,]  2.040415272  0.4083436645 -0.5839441393  0.1167645009
##  [817,]  0.422277993 -0.2392929241 -1.5219378020 -0.2801704929
##  [818,]  2.222438148  0.7828295928  0.1132656344  0.0664286098
##  [819,]  2.536566506  0.4998641083 -0.5070229305  0.3041523799
##  [820,]  0.764170916  0.4403408043 -0.2668126413  0.0017697411
##  [821,]  1.626584603  0.2826285120 -0.7466919579  0.0572906561
##  [822,] -1.287315744 -0.0051380982 -0.7322479331 -0.0056590006
##  [823,] -0.248379102  1.1818877416  1.3925796459 -0.4535007885
##  [824,] -0.301176802 -0.1003577733 -1.1091611305 -0.1970771927
##  [825,] -0.391736998 -2.7058426658 -0.2336039503 -0.2935048057
##  [826,] -1.690154773  0.5312509038  0.3903157091  0.2600750127
##  [827,]  1.888469307  0.6026665993 -0.1734007352  0.0869725543
##  [828,] -0.611852042  0.6155715943  0.3492908063 -0.0776036313
##  [829,]  1.991976537  0.2903418714 -0.8059552475  0.1588397365
##  [830,] -0.980644345  0.8632440423  0.9066167596 -0.0907064609
##  [831,]  1.775803697  0.9037369117  0.4396586320 -0.0177617544
##  [832,]  0.718857287  0.2497411986 -0.6294059092 -0.0485606073
##  [833,] -0.833687139 -2.5745070275  0.1072323590 -0.1411876764
##  [834,]  2.260440877 -1.8017775193  0.9995667308  0.1901909750
##  [835,]  1.337255339  0.8023705821  0.3286442865 -0.0418567368
##  [836,] -1.774999915  0.1474936983 -0.3424681751  0.2279543028
##  [837,]  0.399803256  0.3223881132 -0.4238938582 -0.0701186336
##  [838,] -0.936380515  0.9873496770  1.1426417065 -0.1919920463
##  [839,]  2.179479803 -1.9496163644  0.7276398861  0.1385179118
##  [840,]  3.007587734  0.6876430897 -0.2337647485  0.3411367595
##  [841,] -1.870374160  0.5632092709  0.4869701558  0.3273478706
##  [842,] -1.620610449  0.4614663205  0.2408452781  0.2273380369
##  [843,] -1.023022392 -0.3492787419 -1.4510995830 -0.2951376588
##  [844,] -1.770685763  0.5954920279  0.5315732202  0.2714274578
##  [845,]  1.904973786  0.7327121171  0.0784285267  0.0465846164
##  [846,] -1.591395342  0.4257519598  0.1649955284  0.2394975009
##  [847,]  2.562990804  0.7968981964  0.0699720805  0.2321600030
##  [848,]  2.448714628  0.8098348109  0.1191622895  0.1698070877
##  [849,]  3.439316005  0.6057491448 -0.4825666862  0.5018295425
##  [850,]  1.325410808  0.5247232064 -0.2130330274  0.0160912213
##  [851,] -2.064585965  0.3750610394  0.1550872316  0.4419157522
##  [852,] -1.270831634 -0.0081009142 -0.7414348250  0.0008484596
##  [853,] -0.237987106  1.3098001360  1.6431319218 -0.5733307816
##  [854,]  2.361032923  0.5665144575 -0.3407851422  0.2447449196
##  [855,]  2.329768106  0.8426739392  0.2073056695  0.1488355701
##  [856,] -1.669227253  0.0776180144 -0.4984075380  0.1543765324
##  [857,]  2.122174298  0.7178928761  0.0050411744  0.1175462271
##  [858,]  1.525047644  1.0101725220  0.6993812932 -0.1170107675
##  [859,] -1.485682414  0.7488498410  0.7791125252  0.0811161399
##  [860,]  2.126009898  0.6413522184 -0.1446907270  0.0864714305
##  [861,] -0.215244250 -2.2679155163  0.5828072098 -0.0650239194
##  [862,] -0.830151303 -0.3721395774 -1.5331213440 -0.3316313062
##  [863,]  0.114865431 -0.0540680727 -1.1012975681 -0.1765223549
##  [864,] -1.039427478 -0.2001567792 -1.1587903641 -0.1792721530
##  [865,]  0.189592082  1.0690363805  1.0834071178 -0.3579944511
##  [866,] -2.054663910  0.4622466658  0.3236441072  0.4384648127
##  [867,]  1.671397530  0.6340903128 -0.0683788776  0.0537645154
##  [868,] -1.999511429  0.3731021012  0.1388666250  0.4199836450
##  [869,]  2.731246468  0.7385640913 -0.0773672992  0.2348840688
##  [870,]  1.969118266  0.4985090097 -0.3937557934  0.1246071431
##  [871,] -0.337513664  1.2842380936  1.6127883704 -0.5717425031
##  [872,]  0.535123171  0.9429095692  0.7657989874 -0.2273546168
##  [873,]  1.452114263  0.2842226603 -0.7091709903  0.0603258912
##  [874,] -1.865223934  0.2807446057 -0.0660609278  0.3183069556
##  [875,] -0.025739745 -0.2781888926 -1.5088411669 -0.3096148870
##  [876,]  0.496305932  0.7291602711  0.3532321710 -0.1158610197
##  [877,]  1.054255883  0.8316512012  0.4422478896 -0.0631184354
##  [878,] -0.411139432  0.5047346511  0.0933930243 -0.0981866131
##  [879,] -0.214392747 -0.4181255755 -1.7425906049 -0.4297736850
##  [880,] -1.238466984 -1.6361870113  2.0158575778  0.1282453932
##  [881,] -0.888712772 -0.2038031161 -1.1951268988 -0.2060203744
##  [882,]  2.972601376  0.5529783076 -0.4904362648  0.3562221762
##  [883,] -0.319042954  0.9175777506  0.8845197895 -0.2033995207
##  [884,] -2.177431842  0.4133488394  0.2508323695  0.5078947262
##  [885,] -0.584445282 -2.5839786934  0.0401241403 -0.1717951582
##  [886,]  0.945607898 -2.5262916568 -0.1486264625 -0.2074152378
##  [887,]  0.730940347  0.2196145047 -0.6894456584 -0.1071777225
##  [888,]  2.332972033  0.5665668901 -0.3331847860  0.1526488525
##  [889,]  0.440689837  0.1474303782 -0.7736790271 -0.0855220156
##  [890,]  1.744270485  0.3174712920 -0.7010693455  0.0216148380
##  [891,]  0.513182458 -2.1509374044  0.6673023988 -0.0517576999
##  [892,] -2.102234090  0.3636715954  0.1399692287  0.4555855301
##  [893,]  1.657301836  0.7272110534  0.1181281041 -0.0251997308
##  [894,]  0.457673081  0.0741500082 -0.9185364846 -0.1683565802
##  [895,]  3.373432813  0.5830455387 -0.5132001642  0.4671910550
##  [896,]  2.032276355  0.3639354795 -0.6698348771  0.1489419672
##  [897,] -0.328255504 -0.2670068359 -1.4270396475 -0.3178720101
##  [898,]  1.561043715  0.4167998751 -0.4723473183  0.0998332100
##  [899,] -2.161418582  0.4322760103  0.2849661847  0.4939584313
##  [900,] -0.463411359 -0.3063249432 -1.4774471902 -0.3063604629
##  [901,] -0.150461184 -0.1279512821 -1.1926402596 -0.2084233246
##  [902,]  2.213129897  0.4170516907 -0.6029226110  0.2053816336
##  [903,]  1.876172251  0.7937595000  0.2039745280  0.0224979983
##  [904,] -0.187329921 -2.7230819049 -0.3073816726 -0.3079960149
##  [905,] -1.456756243  0.0615890460 -0.5701289830  0.0793984076
##  [906,] -0.681542804  0.1933733068 -0.4630039086 -0.0453278472
##  [907,] -1.976012455  0.5087866646  0.3999477410  0.3979939668
##  [908,]  3.200311644  0.6227745042 -0.4002938024  0.4183765271
##  [909,] -0.680013377 -2.4169255009  0.3836127106 -0.0787852819
##  [910,] -0.130524791 -2.5063001911  0.1026708573 -0.1890784008
##  [911,]  3.100243750  0.6862269724 -0.2563477811  0.4122658031
##  [912,] -1.855501748  0.5620075408  0.4814872277  0.3365554530
##  [913,]  0.037563168  1.3240372908  1.6170661759 -0.5987722294
##  [914,] -1.051463681 -2.5632134146  0.1710627174 -0.0812036198
##  [915,] -0.066445476 -2.2419160623  0.6048905810 -0.0957891988
##  [916,]  1.562581534  1.0055597726  0.6825312407 -0.0973557726
##  [917,]  0.005022434  0.1528149650 -0.6773176279 -0.0743532975
##  [918,]  0.291831878 -0.1696096431 -1.3610707347 -0.2268250721
##  [919,] -0.337506198  1.1724007756  1.3906571657 -0.4071188898
##  [920,] -1.852374807  0.5571447559  0.4715436592  0.3280380091
##  [921,] -0.598952410  0.0437140690 -0.7705400923 -0.1093096137
##  [922,]  1.581207693  0.7362905590  0.1517700662 -0.0656642316
##  [923,]  0.064352107 -2.3162567041  0.4335883448 -0.0897120376
##  [924,]  0.131277009  0.2852660077 -0.4429733910 -0.0909327836
##  [925,] -0.872901977 -2.5967344690  0.0717841867 -0.1533498350
##  [926,] -0.642461298 -0.0668255623 -0.9764221225 -0.1857608718
##  [927,]  2.737072439  0.6283443228 -0.2947048805  0.2684416459
##  [928,]  0.289252548  0.1543543944 -0.7294585240 -0.1216225295
##  [929,] -0.597043994  0.0479662073 -0.7628414505 -0.0981368143
##  [930,]  0.295272782  0.2608884059 -0.5231700293 -0.0843319404
##  [931,] -0.201092547  1.3683767765  1.7528268987 -0.6897123799
##  [932,] -0.720861909 -2.6347547266 -0.0318613290 -0.1872757597
##  [933,] -1.586777085  0.4204378584  0.1538713537  0.2311532238
##  [934,] -0.757831523 -2.6221003553  0.0002017514 -0.1882438176
##  [935,] -0.985695182 -0.1532439167 -1.0779073164 -0.1691896969
##  [936,]  2.761538392  0.5467136091 -0.4600486051  0.3120785224
##  [937,] -1.774157026  0.6036230675  0.5478227255  0.2870793416
##  [938,] -1.489469632  0.7130220136  0.7086493709  0.1362408515
##  [939,] -1.635417436  0.4686483749  0.2577177091  0.2317432045
##  [940,] -0.109841490  0.1290519626 -0.7009395019 -0.0809912570
##  [941,]  1.594222937  1.0107239990  0.6855887980 -0.0602593721
##  [942,]  2.020968881  0.3909184929 -0.6144771740  0.1313520674
##  [943,] -1.192758099 -0.1490511654 -1.0299161874 -0.1167109041
##  [944,] -2.085159026  0.4485574577  0.3026058761  0.4526589492
##  [945,]  0.759792476 -2.2518652834  0.4219295832 -0.0827485991
##  [946,]  1.097492431 -2.2779460145  0.3041685749 -0.0800448092
##  [947,] -1.182006938  0.8669207342  0.9524006320 -0.0348243195
##  [948,] -1.489737082 -2.2367120583  0.8891760831  0.2377932994
##  [949,] -0.966949186 -0.0860966589 -0.9509328610 -0.1412964984
##  [950,] -0.773495578  0.3443545937 -0.1509377449  0.0141399834
##  [951,] -0.956566434  0.2017682424 -0.3938953196  0.0318539189
##  [952,]  0.138955666 -0.0566124143 -1.1113186655 -0.1629634439
##  [953,] -1.770041822  0.1442182756 -0.3497778328  0.2245053448
##  [954,]  0.023024650  1.3093005709  1.5906064351 -0.5741509567
##  [955,] -1.448095094  0.0581769120 -0.5784939530  0.0786105063
##  [956,] -0.048176408  0.1219639271 -0.7262088718 -0.1172889656
##  [957,]  0.382809605  0.1910093508 -0.6766815486 -0.1028473314
##  [958,] -1.582744705 -2.0021601059  1.3637825614  0.3465073791
##  [959,] -1.705751462  0.6240949082  0.5751382004  0.2489800484
##  [960,] -0.959129446 -2.3167671729  0.6315356869  0.0637824387
##  [961,]  1.347199679 -1.7037073726  1.3766247038 -0.0413473129
##  [962,] -1.753514843  0.1333002000 -0.3741433582  0.2130088182
##  [963,] -0.238289481 -2.7370282588 -0.3245188498 -0.3108040463
##  [964,] -2.027096882  0.5014570136  0.3954543752  0.4100889834
##  [965,] -2.107152008  0.4314334969  0.2731936668  0.4658863165
##  [966,]  1.946124762  0.8941914159  0.3863871768  0.0275454990
##  [967,] -0.876649752 -0.4000471895 -1.5778377486 -0.3625169388
##  [968,] -1.012279856 -0.3563754911 -1.4669371745 -0.3026104011
##  [969,]  1.476775848  0.4027597603 -0.4825157740  0.0700885545
##  [970,]  1.098309169  0.7482257604  0.2707576173 -0.0775367534
##  [971,] -0.401736841 -1.4954627179  2.1312659205 -0.1359564325
##  [972,]  1.358726322  0.7169966215  0.1568054559 -0.0091105262
##  [973,]  3.017669951  0.6392555055 -0.3296746939  0.3092092010
##  [974,] -1.353561963 -0.1309172298 -0.9637890741 -0.0652071262
##  [975,] -0.802218360 -0.0299662256 -0.8748132303 -0.0909577743
##  [976,]  2.652503815 -1.8666299566  0.7947297018  0.2182984851
##  [977,] -0.288206298  0.5369433560  0.1313879884 -0.0659240909
##  [978,] -1.640015899  0.6747687248  0.6620959522  0.2075198270
##  [979,] -1.068402284  0.9417796786  1.0781613633 -0.1224409210
##  [980,] -0.320950109  0.6639010798  0.3864184318 -0.0831255163
##  [981,] -1.077561421 -0.3132490924 -1.3706933490 -0.2571991210
##  [982,] -0.020574489  1.3350075411  1.6504602748 -0.6205426048
##  [983,]  0.538608819 -2.1313347287  0.7007043727 -0.0566099542
##  [984,] -1.390649128  0.3129926870 -0.0930961556  0.1448815820
##  [985,] -2.182389936  0.4166242621  0.2581420271  0.5113436842
##  [986,] -1.450317558  0.7718565412  0.8168727751  0.0919563219
##  [987,] -1.242685039  0.8608802324  0.9524241437 -0.0275034102
##  [988,]  1.352736248  0.6303702934 -0.0115286752 -0.0012366713
##  [989,] -0.403532037  1.1416522918  1.3432350849 -0.3904123568
##  [990,] -1.459926614  0.6427918515  0.5654341352  0.1401006226
##  [991,] -1.814797974  0.4688174039  0.2920959682  0.2973085046
##  [992,] -1.833118709  0.5752063061  0.5033310024  0.3147407406
##  [993,]  0.494162723  0.2455181767 -0.5921999404 -0.0990117343
##  [994,]  0.077984841  0.3799827611 -0.2479698150 -0.0583242240
##  [995,] -0.544750016 -2.7384125860 -0.2673118528 -0.2810191025
##  [996,] -0.124208071  1.3607365835  1.7217598857 -0.6453501650
##  [997,] -1.306221341 -0.1201394316 -0.9519172619 -0.0724872845
##  [998,] -0.632786400 -0.3099770403 -1.4510233731 -0.3111329011
##  [999,]  0.098675866 -2.1823496189  0.6889572366 -0.1070471347
plot(telecom_pca$x,xlim=xlim,ylim=xlim)

telecom_pca$rotation[,1]
##  SeniorCitizen         tenure MonthlyCharges   TotalCharges 
##     0.08960417     0.56498847     0.48563207     0.66099970
telecom_pca$rotation
##                       PC1         PC2         PC3          PC4
## SeniorCitizen  0.08960417 -0.88666415  0.45354733  0.009623196
## tenure         0.56498847  0.31234448  0.51103948 -0.567509999
## MonthlyCharges 0.48563207 -0.32776108 -0.72919909 -0.353557414
## TotalCharges   0.66099970  0.09402283  0.03744529  0.743530060
plot(telecom[,-1])

telecom_pca$x
##                  PC1           PC2           PC3           PC4
##    [1,] -2.015467453  0.3063516984  0.0120502201  0.3952287653
##    [2,] -0.286167867  0.5013439720  0.0615892254 -0.0753083935
##    [3,] -1.580345244  0.0591421382 -0.5512321189  0.1140939064
##    [4,] -0.287614123  0.7983943370  0.6445959152 -0.1696250516
##    [5,] -1.294160708 -0.1237314581 -0.9613547414 -0.0709556042
##    [6,] -0.494044929 -0.3379468993 -1.5326506543 -0.3329395336
##    [7,] -0.020111087  0.0003749667 -0.9685190929 -0.1613687025
##    [8,] -1.733455753  0.4319562059  0.2043525014  0.2789892675
##    [9,]  0.688536938 -0.0510378498 -1.2097481522 -0.1275878542
##   [10,]  0.800699638  0.9284002528  0.6841006823 -0.1865781716
##   [11,] -1.254566657  0.2600970846 -0.2216823424  0.0644229830
##   [12,] -1.764971394  0.6268866250  0.5916904672  0.2774977466
##   [13,]  2.061385552  0.4838318990 -0.4400631575  0.0956542225
##   [14,]  1.724378831  0.3072806955 -0.7177116306  0.0522494039
##   [15,]  0.527494462 -0.1112877649 -1.2945144595 -0.1843081668
##   [16,]  3.161504599  0.5720136417 -0.4917171390  0.4115436863
##   [17,] -0.716173101  1.0901673293  1.3032764892 -0.3397861962
##   [18,]  2.952410314  0.6478858084 -0.2992142283  0.2764189167
##   [19,] -1.254731788  0.1623572800 -0.4124580865  0.0517707540
##   [20,] -0.052469384 -0.0261847489 -1.0136995538 -0.1778530396
##   [21,] -1.611728253 -2.1930906514  0.9970540300  0.3085286329
##   [22,] -1.878281489  0.5620845058  0.4865222098  0.3184532575
##   [23,] -2.175779144  0.4122570318  0.2483958170  0.5067450736
##   [24,]  0.775447113  0.8376438460  0.5105457067 -0.1338228327
##   [25,]  0.410974980  0.7056174597  0.3236927933 -0.0983047154
##   [26,] -0.507827005  0.4543022412  0.0135374770 -0.0810125188
##   [27,]  1.525172980  0.3179618635 -0.6575552351  0.0560433902
##   [28,] -2.009683010  0.3025303719  0.0035222862  0.3912049809
##   [29,]  2.415256278  0.7991045643  0.1058810951  0.1186320774
##   [30,] -0.777763717  0.1696083634 -0.4906300199 -0.0370124895
##   [31,]  2.848230035 -1.6564358066  1.1668468777  0.2246353601
##   [32,] -0.641013427 -2.7867310927 -0.3417486462 -0.3284125213
##   [33,] -0.300560723  0.3117621795 -0.3071772993 -0.0288213652
##   [34,] -2.174952795  0.4117111280  0.2471775407  0.5061702472
##   [35,] -1.519177173 -2.2542318748  0.8606070875  0.2441480838
##   [36,]  2.827024440  0.7296306943 -0.1149545366  0.2914726586
##   [37,] -1.194294975 -0.0682028508 -0.8724635335 -0.0740242687
##   [38,]  0.756572527  0.5250342636 -0.0992482896 -0.0213891894
##   [39,]  0.995843188  0.0282164677 -1.1156929653 -0.1195278411
##   [40,] -0.372576730 -0.2687303412 -1.4222942619 -0.2876389053
##   [41,] -1.361697679  0.2221115384 -0.2755626470  0.1014410539
##   [42,]  1.595061949  0.9430453465  0.5533983805 -0.0736439939
##   [43,] -1.686527850  0.6235121074  0.5699017654  0.2630821071
##   [44,]  1.605413825  0.7377433815  0.1493460653 -0.0429488503
##   [45,] -0.714410979 -0.0113787300 -0.8552542721 -0.1177632548
##   [46,]  1.086026186  0.4712426940 -0.2680799863 -0.0881353262
##   [47,] -1.658263057  0.1090959181 -0.4392579796  0.1648477748
##   [48,] -1.134762350 -0.2330839393 -1.2040775207 -0.1910210350
##   [49,]  1.167167537  0.5738663650 -0.0853678670  0.0005600547
##   [50,]  1.311538924  0.9603726853  0.6458001905 -0.1921306285
##   [51,]  1.264868979 -2.0625593971  0.6907915360 -0.0149786634
##   [52,] -0.168370241 -0.2188635628 -1.3651104889 -0.2895317085
##   [53,] -0.085154857 -2.1475877081  0.7917325457 -0.0363147592
##   [54,] -0.614912060 -2.5298658743  0.1513254615 -0.1432407568
##   [55,]  1.580551201 -1.6543390313  1.4266039081 -0.0209865789
##   [56,]  0.176758767 -2.5201212919  0.0148139888 -0.1829799378
##   [57,]  2.346069747  0.5803719891 -0.3096712143  0.1944602172
##   [58,]  3.020282165 -1.8392739689  0.7738886278  0.2966004227
##   [59,] -1.093507929  0.8111109188  0.8255104785 -0.0206660269
##   [60,]  3.124480162  0.6710979411 -0.2903972792  0.3974064804
##   [61,]  1.531689184  0.3036294823 -0.6862831312  0.0287731236
##   [62,]  1.870638938  0.6140627227 -0.1478439577  0.0985073036
##   [63,]  0.648254123  1.1866591365  1.2240615826 -0.4203028134
##   [64,] -0.961557792  0.2894863205 -0.2211229268  0.0176449277
##   [65,] -0.545892972 -0.2663085838 -1.3834428268 -0.2818011253
##   [66,] -1.169962034 -0.1577506121 -1.0513963954 -0.1181469042
##   [67,]  0.875427786  0.4968895086 -0.1769417601 -0.0595475609
##   [68,]  0.182493361  0.2447198211 -0.5327578437 -0.0720772747
##   [69,] -0.796456606  1.0666790373  1.2727579581 -0.3180565883
##   [70,] -0.750675757 -0.0930231842 -1.0075922102 -0.1228832013
##   [71,] -1.698149465  0.0967246467 -0.4557678685  0.1744954540
##   [72,] -0.700659398  1.0956912830  1.3104807748 -0.3148137478
##   [73,]  3.032428488 -1.8980463204  0.6562547371  0.3124827647
##   [74,] -0.313836135  1.1931437520  1.4280892831 -0.4804957131
##   [75,] -1.364614999 -0.0421342756 -0.7891642665 -0.0121639001
##   [76,]  2.554954116 -2.0261799036  0.5025524213  0.1964623697
##   [77,]  0.197136523  0.6995581852  0.3535888524 -0.0745083433
##   [78,] -1.322542296  0.1413066356 -0.4410049403  0.0890350495
##   [79,]  0.217664019 -2.1274182062  0.7726062771 -0.0961275654
##   [80,] -0.734366957  0.9524571386  1.0342366316 -0.1787310509
##   [81,] -1.197382016 -0.2340930443 -1.1940432895 -0.1738493029
##   [82,] -1.296764834  0.2274303565 -0.2778753067  0.0958974213
##   [83,] -1.008206279 -0.0953456690 -0.9611949560 -0.1256688903
##   [84,]  1.361647046  0.1888972503 -0.8759652645 -0.0193031968
##   [85,] -0.806959336  1.0558336138  1.2528522851 -0.2813738779
##   [86,] -0.448546799 -0.3174794868 -1.5019068907 -0.3197269722
##   [87,] -0.084717836  0.4703519543 -0.0392572419 -0.0536551817
##   [88,] -0.797431545  1.0412029346  1.2214304455 -0.2372032057
##   [89,] -0.891905672  1.0183499064  1.1951683772 -0.2254186136
##   [90,] -1.031259395  0.6564413875  0.5098277540  0.0270728460
##   [91,]  0.227101041  0.2038970410 -0.6216515858 -0.0591512269
##   [92,] -1.032457656 -2.5757692015  0.1430423631 -0.0944246254
##   [93,]  1.987686410  0.7651075091  0.1239313568  0.1167016622
##   [94,]  2.806811496  0.5133466217 -0.5333892179  0.2727432484
##   [95,]  2.903210552  0.7271987352 -0.1359404036  0.3470841182
##   [96,] -0.708173758 -0.0563325608 -0.9437915035 -0.1449897800
##   [97,]  1.543929464  0.9763055519  0.6292716107 -0.1089530202
##   [98,] -2.042972026  0.4566118480  0.3103904728  0.4350686525
##   [99,] -0.686131807  1.0897963793  1.2961226931 -0.3165244945
##  [100,]  0.606006347 -2.4340735414  0.0971351316 -0.1313806771
##  [101,] -2.174952795  0.4117111280  0.2471775407  0.5061702472
##  [102,] -2.187348029  0.4198996847  0.2654516848  0.5147926422
##  [103,]  0.918938002  0.2052854759 -0.7556317176 -0.0585346918
##  [104,]  0.828260114 -1.3164589611  2.2411930707 -0.2766375917
##  [105,]  3.004049207  0.5833891941 -0.4377168502  0.3807084725
##  [106,] -1.994145410  0.4204330920  0.2309257221  0.3922088180
##  [107,]  2.910881473  0.6851658542 -0.2177366027  0.2579300175
##  [108,] -1.044980444  0.7303122424  0.6580689327 -0.0255384601
##  [109,]  1.113535949  0.2883479476 -0.6316082014 -0.0625671835
##  [110,] -0.182569918  1.3696846049  1.7513460190 -0.6718857738
##  [111,]  1.806754913  0.4673260818 -0.4213335735  0.0630347745
##  [112,]  0.473311559  0.7644325971  0.4269041449 -0.1240317493
##  [113,]  1.079176733  0.3192866846 -0.5652398537 -0.0199814513
##  [114,]  0.624327885 -2.0273332320  0.8865403656 -0.0308186348
##  [115,]  0.802448837  0.9679188640  0.7620389149 -0.2349692600
##  [116,] -0.932457938 -0.3170301421 -1.4060826680 -0.2887548140
##  [117,] -0.881816122  0.7789851697  0.7217833082 -0.0630673719
##  [118,] -0.368163059 -0.3092994349 -1.5020791769 -0.3063862092
##  [119,] -1.021001971  0.9439411638  1.0735904064 -0.1492104927
##  [120,]  0.088899116  0.1143871675 -0.7671133245 -0.1638923674
##  [121,]  1.959011199  0.4578647766 -0.4705680350  0.0940391395
##  [122,] -2.026197593  0.4729935049  0.3395070540  0.4159711657
##  [123,] -1.188782751 -0.1484856985 -1.0296909860 -0.1122392064
##  [124,] -1.447591995  0.1665799333 -0.3674576470  0.1157125107
##  [125,] -2.083725783  0.4441172020  0.2938314490  0.4437406886
##  [126,]  0.539725647  0.1848646509 -0.7205916833 -0.0605840051
##  [127,]  0.209918439 -2.2003618683  0.6307395561 -0.0586370421
##  [128,] -0.010898566  1.3390376628  1.6560687648 -0.6036411741
##  [129,] -2.182389936  0.4166242621  0.2581420271  0.5113436842
##  [130,]  1.396133635 -1.3335566399  2.0941270073 -0.2082934779
##  [131,] -0.488380801 -0.1085994906 -1.0891420399 -0.1568600231
##  [132,] -0.576201423  0.3540315690 -0.1703852335 -0.0147272045
##  [133,]  0.757771042  1.0433573449  0.9199122068 -0.3088633185
##  [134,] -1.922916373  0.2452104750 -0.1243967224  0.3308482161
##  [135,] -1.742382162  0.1621482838 -0.3200446092  0.2176521793
##  [136,] -0.791376856  0.9282986842  0.9974460071 -0.1398480704
##  [137,] -0.275699196  0.1604626277 -0.6069323676 -0.0731386512
##  [138,] -0.376504769  1.2566716754  1.5656327046 -0.5261301134
##  [139,] -0.576670736  1.1707003910  1.4342995777 -0.3937585278
##  [140,] -1.102697315 -2.5293673802  0.2465958462 -0.0455643873
##  [141,]  2.637556123 -1.5669191859  1.3842277020  0.1888827841
##  [142,] -1.031083507 -0.0361726080 -0.8419731597 -0.0795512270
##  [143,]  2.224966267  0.5258663614 -0.3905755385  0.1131078737
##  [144,]  1.824074123  0.7191511070  0.0684508781  0.0206287085
##  [145,]  0.223919674 -1.0690561234  2.8500292312 -0.5490385180
##  [146,]  2.412380218  0.6164685312 -0.2521123012  0.1901086577
##  [147,] -2.127246954  0.4451612849  0.3036825113  0.4808911428
##  [148,] -1.754341192  0.1338461038 -0.3729250820  0.2135836445
##  [149,] -0.242980107  0.3699008128 -0.2042353704 -0.0598981756
##  [150,] -0.751647226  0.0909294433 -0.6492204286 -0.0550592777
##  [151,] -1.073099568 -0.0076498994 -0.7785687452 -0.0485870504
##  [152,] -0.640030879 -0.3063633944 -1.4425781495 -0.3087514494
##  [153,]  3.111701929  0.6419525586 -0.3461887078  0.4604697940
##  [154,]  1.786414072  0.6712071826 -0.0178471279  0.0211034744
##  [155,] -2.042218618  0.4839835491  0.3639012414  0.4280368175
##  [156,] -0.565777248 -0.0432490520 -0.9464418700 -0.1404773148
##  [157,] -0.137336369  0.0493816447 -0.8499160814 -0.1442996565
##  [158,] -1.581914961  0.6931113543  0.6875625870  0.1563249540
##  [159,] -0.827824399  0.1591071012 -0.5013908336 -0.0312876590
##  [160,] -1.813761641  0.4742723869  0.3022753840  0.3105090355
##  [161,] -1.105125107  0.2010771358 -0.3662922662  0.0504969156
##  [162,] -0.277685139  0.0339356276 -0.8522100655 -0.1525261096
##  [163,] -1.315154533 -0.1134487617 -0.9372422605 -0.0644836397
##  [164,]  1.019911639  0.6398949025  0.0736162178 -0.0375695116
##  [165,] -1.878916383  0.5420275733  0.4469341284  0.3421662599
##  [166,] -0.242720302  1.3264397073  1.6773555496 -0.6090995206
##  [167,] -1.210277456 -0.0957504472 -0.9230417556 -0.0796099086
##  [168,]  2.362522478  0.8075262451  0.1332558771  0.0954185136
##  [169,]  0.533272788 -1.4299135605  2.0763220454 -0.2129601398
##  [170,] -1.742987721  0.6107737100  0.5562482640  0.2586000645
##  [171,]  0.839076685  0.3833241167 -0.3916082964 -0.0674157512
##  [172,] -0.720591805 -0.4893079825 -1.7815320167 -0.4397049858
##  [173,] -0.540357577 -0.0535656476 -0.9715687177 -0.1434751867
##  [174,]  1.661339506  0.4531497085 -0.4201193144  0.0536221318
##  [175,] -1.279821564  0.8242893656  0.8876622997 -0.0008657922
##  [176,] -1.130555556  0.8091583715  0.8297371924 -0.0548175517
##  [177,] -0.408013662 -2.3527082303  0.4550920136 -0.0634476390
##  [178,] -0.743385170 -2.5017623018  0.2310042629 -0.1128923886
##  [179,] -0.028474511 -0.2818951271 -1.5153215325 -0.3202128601
##  [180,] -0.446593399  1.2140034675  1.4948745044 -0.4700099121
##  [181,] -2.013814755  0.3052598908  0.0096136676  0.3940791126
##  [182,] -1.760125634  0.1376674302 -0.3643971480  0.2176074288
##  [183,] -0.785685539 -0.1784065725 -1.1658501246 -0.2051752464
##  [184,]  0.143094098  0.3168652298 -0.3837755166 -0.0795021588
##  [185,] -0.627242566 -0.0394498337 -0.9274866262 -0.1114766533
##  [186,] -2.098928694  0.3614879802  0.1350961236  0.4532862247
##  [187,] -0.938926300  0.3459076749 -0.1154348647  0.0243347932
##  [188,] -1.945864424  0.3276573170  0.0406986193  0.3599807990
##  [189,] -1.845639560  0.5780694231  0.5114773223  0.3111870300
##  [190,] -0.013645536  0.6008614722  0.2017472848 -0.0492099881
##  [191,]  0.532751459  0.5036226535 -0.0964845987 -0.0404131894
##  [192,] -0.763753011 -0.2802378127 -1.3676905617 -0.2790763147
##  [193,] -0.241701043  1.3285750295  1.6812085557 -0.6034399477
##  [194,]  3.239883891  0.6583217136 -0.3395236129  0.4610277318
##  [195,] -0.529586745  1.2000814152  1.4831787898 -0.4287632277
##  [196,]  0.041504261 -0.1084171375 -1.1921482007 -0.2192149388
##  [197,] -1.423797011  0.6818932760  0.6351992915  0.1183477642
##  [198,]  2.505245073  0.4103612382 -0.6739275213  0.2154787463
##  [199,]  3.255949403  0.6267711577 -0.4031330238  0.4023772523
##  [200,] -2.165862957  0.4057061865  0.2337765017  0.4998471576
##  [201,]  0.513172914 -0.0468538068 -1.1656179976 -0.1890981702
##  [202,] -0.591288638 -0.0355992888 -0.9263805723 -0.1436000171
##  [203,]  2.940458725  0.6614450421 -0.2707942440  0.2975751530
##  [204,] -0.665132866 -0.0322339955 -0.9055964102 -0.1255151563
##  [205,]  0.444015173  0.5408222174 -0.0050303649 -0.0969602015
##  [206,]  0.294475844  0.2693998505 -0.5067690248 -0.0656718236
##  [207,]  1.216941856  1.0904109992  0.9184988127 -0.1822721193
##  [208,] -1.188292177 -0.2400979858 -1.2074443285 -0.1801723925
##  [209,]  0.191402077 -0.2297993808 -1.4572500566 -0.3044790441
##  [210,]  2.513449429  0.5763791191 -0.3517235008  0.2499979911
##  [211,] -1.714650062  0.1441992588 -0.3602215210  0.1992032533
##  [212,] -2.091491554  0.3565748462  0.1241316372  0.4481127878
##  [213,] -0.496532742  1.2175150698  1.5122868829 -0.5021149164
##  [214,] -1.390183335  0.7878346061  0.8373942404  0.0370312003
##  [215,]  0.214739477 -2.3531851542  0.3323793816 -0.1224883096
##  [216,]  0.714439146  0.8348736551  0.5168759742 -0.1193512227
##  [217,]  0.750808255  1.1594496565  1.1501706444 -0.3997181818
##  [218,]  0.986205791  0.9862221755  0.7604665072 -0.1854365658
##  [219,]  1.855475220  0.7342960777  0.0920706096  0.0104623719
##  [220,] -0.869756792 -0.1306549715 -1.0567547514 -0.1643518188
##  [221,] -1.223800243 -0.0877222775 -0.9048314868 -0.0722558497
##  [222,]  0.018466833  1.3179405019  1.6080594762 -0.5582169394
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##  [449,] -0.591232088 -0.2867533777 -1.4141775823 -0.2948348188
##  [450,]  3.021994943  0.6830579553 -0.2455994728  0.3422993016
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##  [452,] -0.209341868 -2.1966241595  0.7204398777 -0.0380387927
##  [453,]  0.848218582  0.8627173863  0.5456990388 -0.1579850044
##  [454,]  0.066115975  0.1755639511 -0.6440909327 -0.1131558173
##  [455,] -0.336113247  1.1786331612  1.4037213320 -0.4615705502
##  [456,]  0.427460789 -0.1169553180 -1.2853346237 -0.2077174875
##  [457,]  0.415018801  0.0679562601 -0.9241517468 -0.0772211680
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##  [468,]  2.469786466  0.8141590330  0.1228861750  0.1965185902
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##  [470,] -1.114668310  0.2003831248 -0.3655677951  0.0412665286
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##  [477,]  0.536500814 -2.0525579928  0.8543294070 -0.0190788094
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##  [483,] -0.028423837 -2.3448391950  0.3960366812 -0.0895563879
##  [484,]  3.184114370  0.6663115833 -0.3123208028  0.4343994170
##  [485,] -0.796080886 -0.1672797593 -1.1424023339 -0.1882858623
##  [486,]  2.252905439  0.8523075736  0.2421691834  0.1090109385
##  [487,] -0.154616411 -0.2308395468 -1.3908982002 -0.3056519804
##  [488,]  2.340036838  0.8102988297  0.1433678740  0.0836645424
##  [489,] -1.280016908 -0.1795026662 -1.0722156623 -0.1163666697
##  [490,]  2.512396435  0.5356958751 -0.4305530109  0.2266058228
##  [491,] -1.494985556  0.0029490050 -0.6767006534  0.0551632265
##  [492,] -1.237622292 -0.1647842795 -1.0517684192 -0.1186799220
##  [493,]  1.267859891 -1.5461613875  1.7014599257 -0.0962765962
##  [494,] -2.171647400  0.4095275129  0.2423044356  0.5038709419
##  [495,] -1.058855892  0.4543663216  0.1200718340  0.0346380592
##  [496,] -0.388707308  0.3782372678 -0.1600257651 -0.0185136216
##  [497,] -0.211680600  1.3415332719  1.7009548083 -0.6196723752
##  [498,] -1.676064236 -2.0162240967  1.3540320509  0.3791472849
##  [499,] -0.281294057 -0.2709420243 -1.4446207224 -0.2891167139
##  [500,]  1.257730880 -0.0658941382 -1.3513446892 -0.1228030889
##  [501,]  2.278696143 -1.5297894937  1.5305557843  0.0548529850
##  [502,]  1.434933438  0.9733438419  0.6455342650 -0.1334176019
##  [503,]  1.268504013  0.5312244136 -0.1884248203 -0.0148250648
##  [504,]  1.920925370  0.8440392592  0.2932045296  0.0330106199
##  [505,]  0.209019199 -2.4789164457  0.0894203126 -0.2030676589
##  [506,] -0.768218171 -0.0616194782 -0.9424670052 -0.1354517117
##  [507,] -0.907988452 -0.3806208401 -1.5340698833 -0.3436118700
##  [508,] -0.942389187 -0.1663238727 -1.1121416212 -0.1641028188
##  [509,] -2.180737238  0.4155324545  0.2557054746  0.5101940316
##  [510,]  0.222646044 -2.4796319030  0.0851319122 -0.1937568110
##  [511,]  2.407741051  0.4802126479 -0.5168510017  0.1562334800
##  [512,] -0.871838925 -2.5108722067  0.2382397447 -0.0972081984
##  [513,]  2.166835286  0.4124569284 -0.6017499108  0.1578198741
##  [514,]  0.518969956  0.0735808325 -0.9327752879 -0.1204672765
##  [515,]  1.275796804  0.1447137337 -0.9447518034 -0.0489658882
##  [516,] -0.565077168  0.4407247539 -0.0030253423 -0.0183301915
##  [517,] -0.950971276 -2.4650718654  0.3425545501 -0.0568466149
##  [518,]  0.104039221 -2.1776060385  0.6968515989 -0.0919880235
##  [519,] -1.855949878  0.5619437973  0.4814618413  0.3360513707
##  [520,]  2.726633388  0.5956142245 -0.3563548668  0.2555524148
##  [521,] -0.374523696 -1.9138287633  1.3054844333 -0.0172428817
##  [522,]  1.472148386  0.5690059691 -0.1556439438  0.0251292071
##  [523,] -0.271709891  0.1530687225 -0.6218874377 -0.0867034619
##  [524,]  0.873523356  0.0944115336 -0.9632211678 -0.0675719682
##  [525,]  1.504387949  0.4692410532 -0.3572348641  0.0338841150
##  [526,]  3.657915782 -1.7893291126  0.7411715082  0.5032311263
##  [527,]  1.897145736  0.5354393211 -0.3064122557  0.0808995548
##  [528,] -1.217553028  0.8738065742  0.9731585577 -0.0477302733
##  [529,]  2.257587627 -1.9278276712  0.7539055291  0.1808899573
##  [530,] -1.500482593  0.7107920465  0.7067604040  0.1223484965
##  [531,] -0.218434082  1.3372554018  1.6942467846 -0.6347908280
##  [532,] -1.137368632 -0.2241664155 -1.1865139261 -0.1728918208
##  [533,]  3.132456689 -1.7873653189  0.8517569544  0.3649002674
##  [534,] -1.104004587 -0.2957801715 -1.3317085083 -0.2388046784
##  [535,] -0.508759846 -0.1686178984 -1.2006935732 -0.2395999977
##  [536,]  1.681474070  0.7260052685  0.1106418290 -0.0085398809
##  [537,] -0.265534027  0.4750241259  0.0054947675 -0.0487320175
##  [538,]  2.542959902  0.7175629035 -0.0814462170  0.2453008437
##  [539,]  1.573912241  0.6952563537  0.0706530929  0.0445414502
##  [540,]  3.329555277  0.6259625162 -0.4204697944  0.4595993658
##  [541,] -1.149886328  0.1368638489 -0.4820895853  0.0083838179
##  [542,] -2.185695331  0.4188078772  0.2630151322  0.5136429896
##  [543,] -0.665396450 -0.1631601264 -1.1596321568 -0.2134956610
##  [544,] -1.323252191  0.3087103092 -0.1142455534  0.1195444407
##  [545,]  0.290128469  0.2914018738 -0.4624028324 -0.0889717641
##  [546,]  0.702260442  0.2992556891 -0.5284702887 -0.0890057069
##  [547,]  2.604507411  0.5641837788 -0.3930390173  0.2257021801
##  [548,]  2.025966641 -2.0434209587  0.5743165887  0.1511561407
##  [549,] -1.779151384  0.6049029925  0.5513350633  0.2859744556
##  [550,]  3.202674133  0.6450675148 -0.3568125881  0.4011198728
##  [551,]  3.362025767  0.5974089062 -0.4818847834  0.4209064894
##  [552,] -0.631283339  1.1475463826  1.3989098473 -0.3506745807
##  [553,] -1.443220224  0.6498755796  0.5768356227  0.0998656887
##  [554,]  0.252550667  0.2487772204 -0.5385754710 -0.0763696748
##  [555,]  0.961174074  0.7279292959  0.2585249782 -0.0941830860
##  [556,] -2.179910889  0.4149865507  0.2544871983  0.5096192052
##  [557,]  0.263281260  0.4357845112 -0.1754111369 -0.0619315910
##  [558,] -0.921399911  0.0200890789 -0.7537908635 -0.0730805508
##  [559,] -1.694017720  0.0939951278 -0.4618592498  0.1716213223
##  [560,]  2.229702111  0.3975152459 -0.6437317244  0.1743794328
##  [561,] -2.054286986  0.4024636418  0.2066085748  0.4426126170
##  [562,] -1.091137141 -0.0348263727 -0.8279982987 -0.0549800251
##  [563,]  2.122587928  0.5131676009 -0.3957788717  0.1415753188
##  [564,] -1.199117557  0.0214663442 -0.6974857740 -0.0139726728
##  [565,]  1.673845329  0.9417095077  0.5354241958 -0.0831643143
##  [566,] -0.053270584 -0.2396443997 -1.4294351101 -0.2443047012
##  [567,]  1.827997486  0.9284739694  0.4771071436  0.0105042169
##  [568,]  0.913308574  0.1067684114 -0.9467170113 -0.0773334725
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##  [571,]  0.544662525 -1.7209054063  1.5027342681 -0.0969280354
##  [572,] -1.025617080  0.0755901997 -0.6255953298 -0.0308487862
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##  [574,]  1.074332370 -2.5032740987 -0.1308792095 -0.1216458624
##  [575,]  1.546446407  0.6947299827  0.0770220702 -0.0483896148
##  [576,]  0.657681147  0.0621928273 -0.9827770719 -0.1046992050
##  [577,] -1.008960174 -0.0150494268 -0.8049630351 -0.0836058633
##  [578,]  1.015632917 -2.2298798083  0.4133892419 -0.0367334917
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##  [584,] -2.120650619  0.4407919984  0.2939354822  0.4762762714
##  [585,] -0.850660892 -2.6958680332 -0.1249784168 -0.2208864184
##  [586,]  0.646164920  0.7186945199  0.3025968154 -0.0890576214
##  [587,] -2.066710087  0.4658407485  0.3330824057  0.4369493931
##  [588,]  2.864111448  0.7448577721 -0.0938772496  0.3557554938
##  [589,]  2.481246350  0.7971493956  0.0865134335  0.2368451888
##  [590,]  3.258766168  0.6318159490 -0.3941178360  0.4160761643
##  [591,] -0.739914165  0.9742884937  1.0785348542 -0.2033806311
##  [592,]  1.830504634  0.7213294677  0.0697458803  0.1004284995
##  [593,]  0.225588535  0.1738268073 -0.6786662511 -0.1285483559
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##  [595,] -1.050844002  0.1244773357 -0.5254829700 -0.0099394510
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##  [602,]  1.582172879  0.8367979518  0.3476514870 -0.0460946531
##  [603,]  1.697947741  0.2097854109 -0.9023847965  0.0190778336
##  [604,]  1.019238499 -0.0296192361 -1.2339546952 -0.0924963473
##  [605,]  2.277235189  0.8272401224  0.1891486453  0.0716913492
##  [606,]  0.541065110  0.3373005640 -0.4228132369 -0.0623694426
##  [607,]  0.088344264  0.8343382509  0.6413331292 -0.2046892586
##  [608,]  3.369738816  0.6124384117 -0.4548809847  0.4611739286
##  [609,]  2.861716043 -1.8287198570  0.8265609058  0.2630114464
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##  [613,]  1.900456036 -2.2222074274  0.2514583020  0.0632679446
##  [614,]  0.724000688  0.6281323774  0.1102487099 -0.0925537933
##  [615,] -1.214170222  0.2991419913 -0.1529405607  0.0459653493
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##  [617,]  2.900554160 -1.7819984831  0.9087960118  0.3304108207
##  [618,]  1.600556406  0.5787728150 -0.1616169279  0.0108979220
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##  [621,]  2.039311129  0.6282299871 -0.1540661748  0.1265587455
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##  [628,]  3.459590282 -1.7631369929  0.8336737304  0.4035000740
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##  [635,]  2.681607106  0.5691796817 -0.4000571567  0.2988891466
##  [636,]  0.688451585  0.0479932180 -1.0164564209 -0.1122086828
##  [637,]  1.588390422  0.9008362273  0.4713860351 -0.0353028724
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##  [641,]  0.082126335  0.6485098439  0.2764906041 -0.0734315177
##  [642,] -1.028806835 -0.3454574155 -1.4425716491 -0.2911138745
##  [643,]  1.524682283 -1.9641862252  0.8314947243 -0.0016717424
##  [644,] -1.665774215  0.5480510351  0.4185980847  0.2480289767
##  [645,]  0.250225114 -2.4790261952  0.0803688095 -0.1702560569
##  [646,] -1.753514843  0.1333002000 -0.3741433582  0.2130088182
##  [647,]  0.733360701  0.6274734379  0.1069836842 -0.0865381702
##  [648,] -0.744266292 -2.7218045559 -0.1957872462 -0.2640351449
##  [649,] -0.105608419 -2.1664830361  0.7586122782 -0.0258688176
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##  [651,] -1.275885164 -0.1822321851 -1.0783070437 -0.1192408014
##  [652,] -1.218584626  0.8670253718  0.9604492332 -0.0639341788
##  [653,] -1.604284883  0.5814714629  0.4720886173  0.2337412753
##  [654,] -1.741017171 -1.8806422082  1.6309401747  0.4253599029
##  [655,] -0.509481193 -0.2610660198 -1.3797806589 -0.3104007714
##  [656,]  2.232972153  0.7543464360  0.0537344779  0.1496974528
##  [657,]  0.812972782  0.4706296311 -0.2165710240 -0.0297982459
##  [658,] -2.153321210  0.4287836828  0.2765692771  0.4925363620
##  [659,] -1.156729662  0.8912095581  0.9962492396 -0.0988715058
##  [660,] -2.018932848  0.4082192097  0.2114759164  0.4143276257
##  [661,] -1.445108950  0.2673032317 -0.1714902402  0.1369894646
##  [662,] -2.177431842  0.4133488394  0.2508323695  0.5078947262
##  [663,]  1.367403811  0.8592609603  0.4350925529 -0.0977733814
##  [664,] -0.579147415  1.1716749926  1.4366894521 -0.3935357362
##  [665,] -1.180627555 -0.1519698011 -1.0380846180 -0.1135962329
##  [666,] -1.313089719 -0.1124916092 -0.9358602014 -0.0606566696
##  [667,] -0.505065310  0.9654233043  1.0156716335 -0.2441607788
##  [668,] -1.643976554  0.1775991819 -0.3087408866  0.1922377337
##  [669,]  1.169102046  1.0337211608  0.8177081552 -0.2097959811
##  [670,] -0.701617260  1.1122044242  1.3436531849 -0.3478401265
##  [671,] -0.523295116  1.0619366735  1.2095349510 -0.3187492060
##  [672,] -1.268448023 -0.1871453191 -1.0892715301 -0.1244142384
##  [673,] -1.484346965  0.6446257899  0.5741714432  0.1246660278
##  [674,]  0.430135923 -1.5517783514  1.8572033882 -0.1538286827
##  [675,]  3.077450325 -1.8657046214  0.7097431120  0.3522378759
##  [676,] -0.691618253  1.0045053521  1.1287478095 -0.2355177432
##  [677,] -1.904570742  0.2671231959 -0.0850704256  0.3255529069
##  [678,] -0.619702252 -0.5127103294 -1.8463272616 -0.4815243489
##  [679,]  0.906755103  0.4494703300 -0.2770429071 -0.0025327888
##  [680,] -1.186639480 -0.2411897934 -1.2098808811 -0.1813220452
##  [681,]  1.390674210  0.7687721536  0.2516354903 -0.0054802042
##  [682,] -1.360962414 -0.0402878268 -0.7864271725 -0.0050465637
##  [683,]  1.516842469 -2.2339028159  0.3055597089  0.0077711199
##  [684,] -1.333729588 -0.1440189205 -0.9930277046 -0.0790029582
##  [685,] -1.684101533  0.0874442824 -0.4764785651  0.1647234063
##  [686,] -0.604423912  1.0442991624  1.1903543312 -0.2844312734
##  [687,] -1.418194032 -2.2835919274  0.7844313479  0.1888948386
##  [688,] -0.389125464  1.0112963117  1.0827018384 -0.2562266775
##  [689,]  1.183898927  0.5184632244 -0.1960822022 -0.0419403422
##  [690,] -2.170821051  0.4089816091  0.2410861593  0.5032961156
##  [691,]  0.074205758  0.2817288957 -0.4389502877 -0.0750416327
##  [692,] -0.834537702  1.0279002426  1.2025478794 -0.2274368430
##  [693,] -1.165519115 -0.1544648505 -1.0460843523 -0.1071318536
##  [694,] -1.342602374 -1.6983571966  1.9137392396  0.1825298350
##  [695,] -2.167515655  0.4067979940  0.2362130542  0.5009968103
##  [696,]  2.317047742  0.8528065875  0.2293566606  0.1616052911
##  [697,] -1.600302648  0.1147498462 -0.4394354471  0.1544698503
##  [698,]  1.321749700 -1.9467372493  0.9053559759  0.0144780602
##  [699,]  1.579207336  0.9953192003  0.6594364020 -0.1072367869
##  [700,]  1.210790517  0.9292660418  0.6036672542 -0.1343938736
##  [701,]  0.439287844  0.2662407856 -0.5409097678 -0.0960510437
##  [702,]  0.234990959  0.1578514027 -0.7126253697 -0.0875274048
##  [703,] -2.142619673  0.4210176552  0.2594642744  0.4835131502
##  [704,] -1.580489627  0.1388616329 -0.3962307580  0.1553381962
##  [705,] -0.082916959  0.1422332785 -0.6801035426 -0.0992017910
##  [706,]  0.997861324  0.9387218314  0.6659107778 -0.2140900186
##  [707,]  0.881378370 -2.4578046481 -0.0042496765 -0.1036552435
##  [708,]  0.006018899  0.2526633607 -0.4826995236 -0.0562528850
##  [709,]  0.069042241  0.1979371552 -0.6005777808 -0.1297783035
##  [710,] -2.185695331  0.4188078772  0.2630151322  0.5136429896
##  [711,] -0.274007379  0.0530352650 -0.8165792443 -0.1062673391
##  [712,] -0.370339377  1.1417296028  1.3362598121 -0.3636058185
##  [713,] -0.479711592 -0.0986783197 -1.0706053234 -0.1971095322
##  [714,]  0.015368512  1.3182264624  1.6107485063 -0.6297554425
##  [715,]  1.191172140  0.3964440509 -0.4377088509  0.0357245498
##  [716,]  1.230004587  1.0457646056  0.8290831544 -0.2033252725
##  [717,]  0.358314608  0.1934961176 -0.6666833808 -0.1168615425
##  [718,] -0.752482592  0.4477768830  0.0476788331 -0.0132972179
##  [719,]  2.179619376 -1.5672928219  1.4758666604  0.0994265889
##  [720,] -2.147970441  0.4249006690  0.2680167757  0.4880247561
##  [721,] -0.430995578  1.2162221541  1.4957581127 -0.4524645966
##  [722,] -0.934586341 -0.2562325912 -1.2882156388 -0.2223063940
##  [723,] -1.685949334  0.1662580307 -0.3228387904  0.2025472441
##  [724,]  0.894142747 -2.2652004934  0.3691505784 -0.0748946393
##  [725,] -1.680623950 -1.8839304789  1.6131892857  0.3966576355
##  [726,] -1.429088383  0.6339094568  0.5418793347  0.1447022075
##  [727,] -1.001909455 -0.1887858413 -1.1436797314 -0.1930882774
##  [728,]  0.679910616 -2.2865750335  0.3699273006 -0.0861411573
##  [729,]  1.543088643  0.8225504448  0.3273917753 -0.0400576963
##  [730,]  1.049696523  0.3921795666 -0.4169607059 -0.0177531697
##  [731,] -2.060438882  0.4634155536  0.3271122236  0.4364818479
##  [732,] -0.186597645  0.1852052282 -0.5759142990 -0.0849492207
##  [733,]  2.048719231  0.8955791003  0.3684967892  0.0433048950
##  [734,]  0.247858324  0.0713168642 -0.8833521309 -0.1340167184
##  [735,] -0.503075603  0.5360450217  0.1713463585 -0.0312524707
##  [736,]  0.907073946 -0.0762188964 -1.3017017490 -0.1487501722
##  [737,]  2.751283546  0.6855582725 -0.1856985633  0.2701728350
##  [738,]  0.922089225 -1.9760377019  0.9278518384 -0.0241116165
##  [739,]  2.745337154 -1.5754721202  1.3447902545  0.2559643959
##  [740,]  0.426971904  0.6175377408  0.1493480543 -0.1457867757
##  [741,] -1.140048192 -0.2311820295 -1.1993166068 -0.1909494481
##  [742,] -0.411986845 -0.2929758992 -1.4615487622 -0.3045337759
##  [743,] -0.302329766  1.1874193162  1.4132256794 -0.4145428661
##  [744,] -1.643972230  0.2081815628 -0.2489471107  0.1918850386
##  [745,]  3.428094186 -1.7563385144  0.8533959977  0.3936454341
##  [746,]  3.586307177 -1.7888998191  0.7573563345  0.4467513047
##  [747,] -0.944158278 -2.5491503654  0.1778102546 -0.1026244725
##  [748,] -0.878537118  1.0482427045  1.2522583356 -0.2863135505
##  [749,]  2.047305030  0.6652564041 -0.0836990854  0.1472279869
##  [750,] -0.518047766  0.4062174657 -0.0803960985  0.0108591034
##  [751,]  1.983285330  0.8529727801  0.2983366483  0.0335989639
##  [752,] -1.064460315 -0.0529255034 -0.8682349912 -0.0746159835
##  [753,] -0.963854549 -0.3374820463 -1.4398228535 -0.2906182365
##  [754,]  0.298740306 -2.5252009458 -0.0180899107 -0.2360314581
##  [755,] -0.345996608  1.2863486833  1.6186332586 -0.5737628477
##  [756,] -2.124387321  0.4422508166  0.2975190655  0.4765860679
##  [757,] -0.428057904 -0.0806525520 -1.0458382932 -0.1844946018
##  [758,]  2.472954157  0.8059848124  0.1066194725  0.1805252313
##  [759,] -2.165036608  0.4051602827  0.2325582254  0.4992723313
##  [760,] -0.029688187 -0.0029776516 -0.9728568960 -0.1766546209
##  [761,] -1.261342692 -0.1044042613 -0.9300642112 -0.0705020059
##  [762,]  1.569625251  0.9893120871  0.6500379624 -0.1285457153
##  [763,] -0.354307039  1.2731613139  1.5937914242 -0.5406315179
##  [764,] -1.594732604  0.3807631152  0.0784460847  0.2045097546
##  [765,] -0.287494106  0.0983480240 -0.7243230568 -0.1537444560
##  [766,] -1.801751759  0.5837119553  0.5142979145  0.2894924882
##  [767,]  0.501000967  0.4492214140 -0.1963638048 -0.0498388712
##  [768,] -0.752287842  0.1719052450 -0.4917170020 -0.0113644777
##  [769,] -1.880369068  0.5438112780  0.4506471001  0.3450452499
##  [770,] -0.256461578 -0.1550976312 -1.2246156388 -0.2156215353
##  [771,] -2.179910889  0.4149865507  0.2544871983  0.5096192052
##  [772,] -0.842846817 -0.2729751119 -1.3383481659 -0.2563660230
##  [773,]  0.653585961  0.1101683639 -0.8874586815 -0.1386034802
##  [774,]  3.236907612  0.6452928753 -0.3637288991  0.4290971829
##  [775,] -1.782117234  0.2195868746 -0.2005127124  0.2463115318
##  [776,] -1.101132029 -0.2462133028 -1.2363297703 -0.1938092032
##  [777,]  2.328374615  0.4429224276 -0.5738844398  0.1474032978
##  [778,] -1.723759091  0.1515283635 -0.3442913921  0.2085134569
##  [779,]  1.766798933  0.9217592201  0.4774355433 -0.0538223436
##  [780,] -1.626503007  0.2007147476 -0.2669338159  0.1889701559
##  [781,] -0.590954027  0.4217214443 -0.0351877482 -0.0124803322
##  [782,] -1.646089483  0.0623327085 -0.5325192736  0.1382813951
##  [783,]  0.311061105  1.0744357382  1.0691161408 -0.3179951819
##  [784,]  1.953432764 -2.1986226649  0.2880204495  0.0198482236
##  [785,]  1.157955043  1.0840108551  0.9189525063 -0.2441107897
##  [786,] -0.189852042  0.4632954375 -0.0316314372 -0.0843062233
##  [787,] -0.182131386  0.1380091505 -0.6683471199 -0.1186808761
##  [788,]  1.658299685  0.9647724373  0.5842163662 -0.1130433018
##  [789,]  0.844790437  0.8668738805  0.5543604557 -0.1513107229
##  [790,]  1.718097422  0.8396726159  0.3269232479 -0.0699231335
##  [791,] -1.984661766  0.5088832504  0.4019879391  0.3912734316
##  [792,]  0.017621739  0.4025784924 -0.1919301933 -0.0555195966
##  [793,] -1.577856377  0.2143321025 -0.2499276651  0.1891764723
##  [794,] -1.402019743 -0.0528256539 -0.8030033935  0.0032839973
##  [795,]  0.237963047  0.2194376944 -0.5928699404 -0.0848993476
##  [796,] -1.514484261  0.6123477494  0.5161315444  0.1666985309
##  [797,] -2.178258191  0.4138947432  0.2520506458  0.5084695526
##  [798,]  2.222486439  0.5919214960 -0.2626077093  0.1911957956
##  [799,]  2.097419072 -1.4979183454  1.6287497737  0.0513784138
##  [800,] -0.398429662 -0.2903840332 -1.4595156664 -0.2877795344
##  [801,] -0.995556301  0.8870605562  0.9567099166 -0.1183682895
##  [802,]  0.428675364  0.6190437099  0.1503752716 -0.0713042397
##  [803,] -0.867509713 -0.2200270682 -1.2306133233 -0.2257961353
##  [804,]  1.936363311  0.9094523048  0.4190608681 -0.0153836574
##  [805,] -0.919366763  0.2848725717 -0.2389742433  0.0410341867
##  [806,]  3.050031277  0.6372242254 -0.3404923268  0.3305675558
##  [807,]  1.213514445  0.1822957316 -0.8597238709 -0.0137200857
##  [808,] -1.359346405 -0.1270959033 -0.9552611401 -0.0611833419
##  [809,]  2.205777418  0.4658907919 -0.5052585676  0.1708220713
##  [810,]  2.847600120  0.6594518806 -0.2561475903  0.2882541588
##  [811,] -0.844588905  0.9173491609  0.9865066702 -0.1376680767
##  [812,] -0.992189274  0.7532071641  0.6933554800 -0.0706712578
##  [813,] -1.823130668 -1.9256843203  1.5582356836  0.4664494989
##  [814,]  0.015231636  0.0931668542 -0.7947268842 -0.1317119758
##  [815,] -1.034653249 -0.2924866378 -1.3388312167 -0.2453955409
##  [816,]  2.040415272  0.4083436645 -0.5839441393  0.1167645009
##  [817,]  0.422277993 -0.2392929241 -1.5219378020 -0.2801704929
##  [818,]  2.222438148  0.7828295928  0.1132656344  0.0664286098
##  [819,]  2.536566506  0.4998641083 -0.5070229305  0.3041523799
##  [820,]  0.764170916  0.4403408043 -0.2668126413  0.0017697411
##  [821,]  1.626584603  0.2826285120 -0.7466919579  0.0572906561
##  [822,] -1.287315744 -0.0051380982 -0.7322479331 -0.0056590006
##  [823,] -0.248379102  1.1818877416  1.3925796459 -0.4535007885
##  [824,] -0.301176802 -0.1003577733 -1.1091611305 -0.1970771927
##  [825,] -0.391736998 -2.7058426658 -0.2336039503 -0.2935048057
##  [826,] -1.690154773  0.5312509038  0.3903157091  0.2600750127
##  [827,]  1.888469307  0.6026665993 -0.1734007352  0.0869725543
##  [828,] -0.611852042  0.6155715943  0.3492908063 -0.0776036313
##  [829,]  1.991976537  0.2903418714 -0.8059552475  0.1588397365
##  [830,] -0.980644345  0.8632440423  0.9066167596 -0.0907064609
##  [831,]  1.775803697  0.9037369117  0.4396586320 -0.0177617544
##  [832,]  0.718857287  0.2497411986 -0.6294059092 -0.0485606073
##  [833,] -0.833687139 -2.5745070275  0.1072323590 -0.1411876764
##  [834,]  2.260440877 -1.8017775193  0.9995667308  0.1901909750
##  [835,]  1.337255339  0.8023705821  0.3286442865 -0.0418567368
##  [836,] -1.774999915  0.1474936983 -0.3424681751  0.2279543028
##  [837,]  0.399803256  0.3223881132 -0.4238938582 -0.0701186336
##  [838,] -0.936380515  0.9873496770  1.1426417065 -0.1919920463
##  [839,]  2.179479803 -1.9496163644  0.7276398861  0.1385179118
##  [840,]  3.007587734  0.6876430897 -0.2337647485  0.3411367595
##  [841,] -1.870374160  0.5632092709  0.4869701558  0.3273478706
##  [842,] -1.620610449  0.4614663205  0.2408452781  0.2273380369
##  [843,] -1.023022392 -0.3492787419 -1.4510995830 -0.2951376588
##  [844,] -1.770685763  0.5954920279  0.5315732202  0.2714274578
##  [845,]  1.904973786  0.7327121171  0.0784285267  0.0465846164
##  [846,] -1.591395342  0.4257519598  0.1649955284  0.2394975009
##  [847,]  2.562990804  0.7968981964  0.0699720805  0.2321600030
##  [848,]  2.448714628  0.8098348109  0.1191622895  0.1698070877
##  [849,]  3.439316005  0.6057491448 -0.4825666862  0.5018295425
##  [850,]  1.325410808  0.5247232064 -0.2130330274  0.0160912213
##  [851,] -2.064585965  0.3750610394  0.1550872316  0.4419157522
##  [852,] -1.270831634 -0.0081009142 -0.7414348250  0.0008484596
##  [853,] -0.237987106  1.3098001360  1.6431319218 -0.5733307816
##  [854,]  2.361032923  0.5665144575 -0.3407851422  0.2447449196
##  [855,]  2.329768106  0.8426739392  0.2073056695  0.1488355701
##  [856,] -1.669227253  0.0776180144 -0.4984075380  0.1543765324
##  [857,]  2.122174298  0.7178928761  0.0050411744  0.1175462271
##  [858,]  1.525047644  1.0101725220  0.6993812932 -0.1170107675
##  [859,] -1.485682414  0.7488498410  0.7791125252  0.0811161399
##  [860,]  2.126009898  0.6413522184 -0.1446907270  0.0864714305
##  [861,] -0.215244250 -2.2679155163  0.5828072098 -0.0650239194
##  [862,] -0.830151303 -0.3721395774 -1.5331213440 -0.3316313062
##  [863,]  0.114865431 -0.0540680727 -1.1012975681 -0.1765223549
##  [864,] -1.039427478 -0.2001567792 -1.1587903641 -0.1792721530
##  [865,]  0.189592082  1.0690363805  1.0834071178 -0.3579944511
##  [866,] -2.054663910  0.4622466658  0.3236441072  0.4384648127
##  [867,]  1.671397530  0.6340903128 -0.0683788776  0.0537645154
##  [868,] -1.999511429  0.3731021012  0.1388666250  0.4199836450
##  [869,]  2.731246468  0.7385640913 -0.0773672992  0.2348840688
##  [870,]  1.969118266  0.4985090097 -0.3937557934  0.1246071431
##  [871,] -0.337513664  1.2842380936  1.6127883704 -0.5717425031
##  [872,]  0.535123171  0.9429095692  0.7657989874 -0.2273546168
##  [873,]  1.452114263  0.2842226603 -0.7091709903  0.0603258912
##  [874,] -1.865223934  0.2807446057 -0.0660609278  0.3183069556
##  [875,] -0.025739745 -0.2781888926 -1.5088411669 -0.3096148870
##  [876,]  0.496305932  0.7291602711  0.3532321710 -0.1158610197
##  [877,]  1.054255883  0.8316512012  0.4422478896 -0.0631184354
##  [878,] -0.411139432  0.5047346511  0.0933930243 -0.0981866131
##  [879,] -0.214392747 -0.4181255755 -1.7425906049 -0.4297736850
##  [880,] -1.238466984 -1.6361870113  2.0158575778  0.1282453932
##  [881,] -0.888712772 -0.2038031161 -1.1951268988 -0.2060203744
##  [882,]  2.972601376  0.5529783076 -0.4904362648  0.3562221762
##  [883,] -0.319042954  0.9175777506  0.8845197895 -0.2033995207
##  [884,] -2.177431842  0.4133488394  0.2508323695  0.5078947262
##  [885,] -0.584445282 -2.5839786934  0.0401241403 -0.1717951582
##  [886,]  0.945607898 -2.5262916568 -0.1486264625 -0.2074152378
##  [887,]  0.730940347  0.2196145047 -0.6894456584 -0.1071777225
##  [888,]  2.332972033  0.5665668901 -0.3331847860  0.1526488525
##  [889,]  0.440689837  0.1474303782 -0.7736790271 -0.0855220156
##  [890,]  1.744270485  0.3174712920 -0.7010693455  0.0216148380
##  [891,]  0.513182458 -2.1509374044  0.6673023988 -0.0517576999
##  [892,] -2.102234090  0.3636715954  0.1399692287  0.4555855301
##  [893,]  1.657301836  0.7272110534  0.1181281041 -0.0251997308
##  [894,]  0.457673081  0.0741500082 -0.9185364846 -0.1683565802
##  [895,]  3.373432813  0.5830455387 -0.5132001642  0.4671910550
##  [896,]  2.032276355  0.3639354795 -0.6698348771  0.1489419672
##  [897,] -0.328255504 -0.2670068359 -1.4270396475 -0.3178720101
##  [898,]  1.561043715  0.4167998751 -0.4723473183  0.0998332100
##  [899,] -2.161418582  0.4322760103  0.2849661847  0.4939584313
##  [900,] -0.463411359 -0.3063249432 -1.4774471902 -0.3063604629
##  [901,] -0.150461184 -0.1279512821 -1.1926402596 -0.2084233246
##  [902,]  2.213129897  0.4170516907 -0.6029226110  0.2053816336
##  [903,]  1.876172251  0.7937595000  0.2039745280  0.0224979983
##  [904,] -0.187329921 -2.7230819049 -0.3073816726 -0.3079960149
##  [905,] -1.456756243  0.0615890460 -0.5701289830  0.0793984076
##  [906,] -0.681542804  0.1933733068 -0.4630039086 -0.0453278472
##  [907,] -1.976012455  0.5087866646  0.3999477410  0.3979939668
##  [908,]  3.200311644  0.6227745042 -0.4002938024  0.4183765271
##  [909,] -0.680013377 -2.4169255009  0.3836127106 -0.0787852819
##  [910,] -0.130524791 -2.5063001911  0.1026708573 -0.1890784008
##  [911,]  3.100243750  0.6862269724 -0.2563477811  0.4122658031
##  [912,] -1.855501748  0.5620075408  0.4814872277  0.3365554530
##  [913,]  0.037563168  1.3240372908  1.6170661759 -0.5987722294
##  [914,] -1.051463681 -2.5632134146  0.1710627174 -0.0812036198
##  [915,] -0.066445476 -2.2419160623  0.6048905810 -0.0957891988
##  [916,]  1.562581534  1.0055597726  0.6825312407 -0.0973557726
##  [917,]  0.005022434  0.1528149650 -0.6773176279 -0.0743532975
##  [918,]  0.291831878 -0.1696096431 -1.3610707347 -0.2268250721
##  [919,] -0.337506198  1.1724007756  1.3906571657 -0.4071188898
##  [920,] -1.852374807  0.5571447559  0.4715436592  0.3280380091
##  [921,] -0.598952410  0.0437140690 -0.7705400923 -0.1093096137
##  [922,]  1.581207693  0.7362905590  0.1517700662 -0.0656642316
##  [923,]  0.064352107 -2.3162567041  0.4335883448 -0.0897120376
##  [924,]  0.131277009  0.2852660077 -0.4429733910 -0.0909327836
##  [925,] -0.872901977 -2.5967344690  0.0717841867 -0.1533498350
##  [926,] -0.642461298 -0.0668255623 -0.9764221225 -0.1857608718
##  [927,]  2.737072439  0.6283443228 -0.2947048805  0.2684416459
##  [928,]  0.289252548  0.1543543944 -0.7294585240 -0.1216225295
##  [929,] -0.597043994  0.0479662073 -0.7628414505 -0.0981368143
##  [930,]  0.295272782  0.2608884059 -0.5231700293 -0.0843319404
##  [931,] -0.201092547  1.3683767765  1.7528268987 -0.6897123799
##  [932,] -0.720861909 -2.6347547266 -0.0318613290 -0.1872757597
##  [933,] -1.586777085  0.4204378584  0.1538713537  0.2311532238
##  [934,] -0.757831523 -2.6221003553  0.0002017514 -0.1882438176
##  [935,] -0.985695182 -0.1532439167 -1.0779073164 -0.1691896969
##  [936,]  2.761538392  0.5467136091 -0.4600486051  0.3120785224
##  [937,] -1.774157026  0.6036230675  0.5478227255  0.2870793416
##  [938,] -1.489469632  0.7130220136  0.7086493709  0.1362408515
##  [939,] -1.635417436  0.4686483749  0.2577177091  0.2317432045
##  [940,] -0.109841490  0.1290519626 -0.7009395019 -0.0809912570
##  [941,]  1.594222937  1.0107239990  0.6855887980 -0.0602593721
##  [942,]  2.020968881  0.3909184929 -0.6144771740  0.1313520674
##  [943,] -1.192758099 -0.1490511654 -1.0299161874 -0.1167109041
##  [944,] -2.085159026  0.4485574577  0.3026058761  0.4526589492
##  [945,]  0.759792476 -2.2518652834  0.4219295832 -0.0827485991
##  [946,]  1.097492431 -2.2779460145  0.3041685749 -0.0800448092
##  [947,] -1.182006938  0.8669207342  0.9524006320 -0.0348243195
##  [948,] -1.489737082 -2.2367120583  0.8891760831  0.2377932994
##  [949,] -0.966949186 -0.0860966589 -0.9509328610 -0.1412964984
##  [950,] -0.773495578  0.3443545937 -0.1509377449  0.0141399834
##  [951,] -0.956566434  0.2017682424 -0.3938953196  0.0318539189
##  [952,]  0.138955666 -0.0566124143 -1.1113186655 -0.1629634439
##  [953,] -1.770041822  0.1442182756 -0.3497778328  0.2245053448
##  [954,]  0.023024650  1.3093005709  1.5906064351 -0.5741509567
##  [955,] -1.448095094  0.0581769120 -0.5784939530  0.0786105063
##  [956,] -0.048176408  0.1219639271 -0.7262088718 -0.1172889656
##  [957,]  0.382809605  0.1910093508 -0.6766815486 -0.1028473314
##  [958,] -1.582744705 -2.0021601059  1.3637825614  0.3465073791
##  [959,] -1.705751462  0.6240949082  0.5751382004  0.2489800484
##  [960,] -0.959129446 -2.3167671729  0.6315356869  0.0637824387
##  [961,]  1.347199679 -1.7037073726  1.3766247038 -0.0413473129
##  [962,] -1.753514843  0.1333002000 -0.3741433582  0.2130088182
##  [963,] -0.238289481 -2.7370282588 -0.3245188498 -0.3108040463
##  [964,] -2.027096882  0.5014570136  0.3954543752  0.4100889834
##  [965,] -2.107152008  0.4314334969  0.2731936668  0.4658863165
##  [966,]  1.946124762  0.8941914159  0.3863871768  0.0275454990
##  [967,] -0.876649752 -0.4000471895 -1.5778377486 -0.3625169388
##  [968,] -1.012279856 -0.3563754911 -1.4669371745 -0.3026104011
##  [969,]  1.476775848  0.4027597603 -0.4825157740  0.0700885545
##  [970,]  1.098309169  0.7482257604  0.2707576173 -0.0775367534
##  [971,] -0.401736841 -1.4954627179  2.1312659205 -0.1359564325
##  [972,]  1.358726322  0.7169966215  0.1568054559 -0.0091105262
##  [973,]  3.017669951  0.6392555055 -0.3296746939  0.3092092010
##  [974,] -1.353561963 -0.1309172298 -0.9637890741 -0.0652071262
##  [975,] -0.802218360 -0.0299662256 -0.8748132303 -0.0909577743
##  [976,]  2.652503815 -1.8666299566  0.7947297018  0.2182984851
##  [977,] -0.288206298  0.5369433560  0.1313879884 -0.0659240909
##  [978,] -1.640015899  0.6747687248  0.6620959522  0.2075198270
##  [979,] -1.068402284  0.9417796786  1.0781613633 -0.1224409210
##  [980,] -0.320950109  0.6639010798  0.3864184318 -0.0831255163
##  [981,] -1.077561421 -0.3132490924 -1.3706933490 -0.2571991210
##  [982,] -0.020574489  1.3350075411  1.6504602748 -0.6205426048
##  [983,]  0.538608819 -2.1313347287  0.7007043727 -0.0566099542
##  [984,] -1.390649128  0.3129926870 -0.0930961556  0.1448815820
##  [985,] -2.182389936  0.4166242621  0.2581420271  0.5113436842
##  [986,] -1.450317558  0.7718565412  0.8168727751  0.0919563219
##  [987,] -1.242685039  0.8608802324  0.9524241437 -0.0275034102
##  [988,]  1.352736248  0.6303702934 -0.0115286752 -0.0012366713
##  [989,] -0.403532037  1.1416522918  1.3432350849 -0.3904123568
##  [990,] -1.459926614  0.6427918515  0.5654341352  0.1401006226
##  [991,] -1.814797974  0.4688174039  0.2920959682  0.2973085046
##  [992,] -1.833118709  0.5752063061  0.5033310024  0.3147407406
##  [993,]  0.494162723  0.2455181767 -0.5921999404 -0.0990117343
##  [994,]  0.077984841  0.3799827611 -0.2479698150 -0.0583242240
##  [995,] -0.544750016 -2.7384125860 -0.2673118528 -0.2810191025
##  [996,] -0.124208071  1.3607365835  1.7217598857 -0.6453501650
##  [997,] -1.306221341 -0.1201394316 -0.9519172619 -0.0724872845
##  [998,] -0.632786400 -0.3099770403 -1.4510233731 -0.3111329011
##  [999,]  0.098675866 -2.1823496189  0.6889572366 -0.1070471347
plot(telecom_pca)

#get the original value of the data based on PCA
center <- telecom_pca$center
scale <- telecom_pca$scale
new_telecom <- as.matrix(telecom[,-1])
new_telecom
##         SeniorCitizen tenure MonthlyCharges TotalCharges
##    [1,]             0      1          29.85        29.85
##    [2,]             0     34          56.95      1889.50
##    [3,]             0      2          53.85       108.15
##    [4,]             0     45          42.30      1840.75
##    [5,]             0      2          70.70       151.65
##    [6,]             0      8          99.65       820.50
##    [7,]             0     22          89.10      1949.40
##    [8,]             0     10          29.75       301.90
##    [9,]             0     28         104.80      3046.05
##   [10,]             0     62          56.15      3487.95
##   [11,]             0     13          49.95       587.45
##   [12,]             0     16          18.95       326.80
##   [13,]             0     58         100.35      5681.10
##   [14,]             0     49         103.70      5036.30
##   [15,]             0     25         105.50      2686.05
##   [16,]             0     69         113.25      7895.15
##   [17,]             0     52          20.65      1022.95
##   [18,]             0     71         106.70      7382.25
##   [19,]             0     10          55.20       528.35
##   [20,]             0     21          90.05      1862.90
##   [21,]             1      1          39.65        39.65
##   [22,]             0     12          19.80       202.25
##   [23,]             0      1          20.15        20.15
##   [24,]             0     58          59.90      3505.10
##   [25,]             0     49          59.60      2970.30
##   [26,]             0     30          55.30      1530.60
##   [27,]             0     47          99.35      4749.15
##   [28,]             0      1          30.20        30.20
##   [29,]             0     72          90.25      6369.45
##   [30,]             0     17          64.70      1093.10
##   [31,]             1     71          96.35      6766.95
##   [32,]             1      2          95.50       181.65
##   [33,]             0     27          66.15      1874.45
##   [34,]             0      1          20.20        20.20
##   [35,]             1      1          45.25        45.25
##   [36,]             0     72          99.90      7251.70
##   [37,]             0      5          69.70       316.90
##   [38,]             0     46          74.80      3548.30
##   [39,]             0     34         106.35      3549.25
##   [40,]             0     11          97.85      1105.40
##   [41,]             0     10          49.55       475.70
##   [42,]             0     70          69.20      4872.35
##   [43,]             0     17          20.75       418.25
##   [44,]             0     63          79.85      4861.45
##   [45,]             0     13          76.20       981.45
##   [46,]             0     49          84.50      3906.70
##   [47,]             0      2          49.25        97.00
##   [48,]             0      2          80.65       144.15
##   [49,]             0     52          79.75      4217.80
##   [50,]             0     69          64.15      4254.10
##   [51,]             1     43          90.25      3838.75
##   [52,]             0     15          99.10      1426.40
##   [53,]             1     25          69.50      1752.65
##   [54,]             1      8          80.65       633.30
##   [55,]             1     60          74.85      4456.35
##   [56,]             1     18          95.45      1752.55
##   [57,]             0     63          99.65      6311.20
##   [58,]             1     66         108.45      7076.35
##   [59,]             0     34          24.95       894.30
##   [60,]             0     72         107.50      7853.70
##   [61,]             0     47         100.50      4707.10
##   [62,]             0     60          89.90      5450.70
##   [63,]             0     72          42.10      2962.00
##   [64,]             0     18          54.40       957.10
##   [65,]             0      9          94.40       857.25
##   [66,]             0      3          75.30       244.10
##   [67,]             0     47          78.90      3650.35
##   [68,]             0     31          79.20      2497.20
##   [69,]             0     50          20.15       930.90
##   [70,]             0     10          79.85       887.35
##   [71,]             0      1          49.05        49.05
##   [72,]             0     52          20.40      1090.65
##   [73,]             1     64         111.60      7099.00
##   [74,]             0     62          24.25      1424.60
##   [75,]             0      3          64.50       177.40
##   [76,]             1     56         110.50      6139.50
##   [77,]             0     46          55.65      2688.85
##   [78,]             0      8          54.65       482.25
##   [79,]             1     30          74.75      2111.30
##   [80,]             0     45          25.90      1216.60
##   [81,]             0      1          79.35        79.35
##   [82,]             0     11          50.55       565.35
##   [83,]             0      7          75.15       496.90
##   [84,]             0     42         103.80      4327.50
##   [85,]             0     49          20.15       973.35
##   [86,]             0      9          99.30       918.75
##   [87,]             0     35          62.15      2215.45
##   [88,]             0     48          20.65      1057.00
##   [89,]             0     46          19.95       927.10
##   [90,]             0     29          33.75      1009.25
##   [91,]             0     30          82.05      2570.20
##   [92,]             1      1          74.70        74.70
##   [93,]             0     66          84.00      5714.25
##   [94,]             0     65         111.05      7107.00
##   [95,]             0     72         100.90      7459.05
##   [96,]             0     12          78.95       927.35
##   [97,]             0     71          66.85      4748.70
##   [98,]             0      5          21.05       113.85
##   [99,]             0     52          21.00      1107.20
##  [100,]             1     25          98.50      2514.50
##  [101,]             0      1          20.20        20.20
##  [102,]             0      1          19.45        19.45
##  [103,]             0     38          95.00      3605.60
##  [104,]             1     66          45.55      3027.25
##  [105,]             0     68         110.00      7611.85
##  [106,]             0      5          24.30       100.20
##  [107,]             0     72         104.15      7303.05
##  [108,]             0     32          30.15       927.65
##  [109,]             0     43          94.35      3921.30
##  [110,]             0     72          19.40      1363.25
##  [111,]             0     55          96.75      5238.90
##  [112,]             0     52          57.95      3042.25
##  [113,]             0     43          91.65      3954.10
##  [114,]             1     37          76.50      2868.15
##  [115,]             0     64          54.60      3423.50
##  [116,]             0      3          89.85       248.40
##  [117,]             0     36          31.05      1126.35
##  [118,]             0     10         100.25      1064.65
##  [119,]             0     41          20.65       835.15
##  [120,]             0     27          85.20      2151.60
##  [121,]             0     56          99.80      5515.45
##  [122,]             0      6          20.70       112.75
##  [123,]             0      3          74.40       229.55
##  [124,]             0      7          50.70       350.35
##  [125,]             0      4          20.85        62.90
##  [126,]             0     33          88.95      3027.65
##  [127,]             1     27          78.05      2135.50
##  [128,]             0     72          23.55      1723.95
##  [129,]             0      1          19.75        19.75
##  [130,]             1     71          56.45      3985.35
##  [131,]             0     13          85.95      1215.65
##  [132,]             0     25          58.60      1502.65
##  [133,]             0     67          50.55      3260.10
##  [134,]             0      1          35.45        35.45
##  [135,]             0      2          44.35        81.25
##  [136,]             0     43          25.70      1188.20
##  [137,]             0     23          75.00      1778.50
##  [138,]             0     64          20.20      1277.75
##  [139,]             0     57          19.60      1170.55
##  [140,]             1      1          70.45        70.45
##  [141,]             1     72          88.05      6425.65
##  [142,]             0      8          71.15       563.65
##  [143,]             0     61         101.05      5971.25
##  [144,]             0     64          84.30      5289.05
##  [145,]             1     71          23.95      1756.20
##  [146,]             0     65          99.05      6416.70
##  [147,]             0      3          19.60        61.35
##  [148,]             0      1          45.65        45.65
##  [149,]             0     30          64.50      1929.95
##  [150,]             0     15          69.50      1071.40
##  [151,]             0      8          68.55       564.35
##  [152,]             0      7          95.00       655.50
##  [153,]             0     70         108.15      7930.55
##  [154,]             0     62          86.10      5215.25
##  [155,]             0      6          19.70       113.50
##  [156,]             0     14          80.90      1152.80
##  [157,]             0     22          84.15      1821.95
##  [158,]             0     22          20.15       419.90
##  [159,]             0     16          64.25      1024.00
##  [160,]             0     10          25.70       251.60
##  [161,]             0     13          56.00       764.55
##  [162,]             0     20          82.40      1592.35
##  [163,]             0      2          69.70       135.20
##  [164,]             0     53          73.90      3958.25
##  [165,]             0     11          20.60       233.90
##  [166,]             0     69          19.90      1363.45
##  [167,]             0      4          70.90       273.00
##  [168,]             0     72          89.05      6254.45
##  [169,]             1     58          45.30      2651.20
##  [170,]             0     16          20.40       321.40
##  [171,]             0     43          84.25      3539.25
##  [172,]             0      2         104.40       242.80
##  [173,]             0     14          81.95      1181.75
##  [174,]             0     53          94.85      5000.20
##  [175,]             0     32          20.55       654.55
##  [176,]             0     34          24.70       780.20
##  [177,]             1     15          74.45      1145.70
##  [178,]             1      7          76.45       503.60
##  [179,]             0     15         105.35      1559.25
##  [180,]             0     61          20.55      1252.00
##  [181,]             0      1          29.95        29.95
##  [182,]             0      1          45.30        45.30
##  [183,]             0      8          84.50       662.65
##  [184,]             0     33          74.75      2453.30
##  [185,]             0     13          79.25      1111.65
##  [186,]             0      1          24.80        24.80
##  [187,]             0     20          51.80      1023.85
##  [188,]             0      3          30.40        82.15
##  [189,]             0     13          19.65       244.80
##  [190,]             0     40          56.60      2379.10
##  [191,]             0     43          71.90      3173.35
##  [192,]             0      6          91.00       531.00
##  [193,]             0     69          19.75      1375.40
##  [194,]             0     72         109.70      8129.30
##  [195,]             0     59          19.30      1192.70
##  [196,]             0     20          96.55      1901.65
##  [197,]             0     24          24.10       587.40
##  [198,]             0     59         111.35      6519.75
##  [199,]             0     72         112.25      8041.65
##  [200,]             0      1          20.75        20.75
##  [201,]             0     27         101.90      2681.15
##  [202,]             0     14          80.05      1112.30
##  [203,]             0     71         105.55      7405.50
##  [204,]             0     13          78.30      1033.95
##  [205,]             0     44          68.85      2958.95
##  [206,]             0     33          79.95      2684.85
##  [207,]             0     72          55.45      4179.20
##  [208,]             0      1          79.90        79.90
##  [209,]             0     19         106.60      1934.45
##  [210,]             0     64         102.45      6654.10
##  [211,]             0      2          46.00        84.50
##  [212,]             0      1          25.25        25.25
##  [213,]             0     61          19.75      1124.20
##  [214,]             0     29          20.00       540.05
##  [215,]             1     23          86.80      1975.85
##  [216,]             0     57          58.75      3437.45
##  [217,]             0     72          45.25      3139.80
##  [218,]             0     66          56.60      3789.20
##  [219,]             0     65          84.20      5324.50
##  [220,]             0      8          80.00       624.60
##  [221,]             0      4          70.15       268.35
##  [222,]             0     71          24.75      1836.90
##  [223,]             0      1          20.20        20.20
##  [224,]             0      4          50.05       179.35
##  [225,]             0     12          19.35       219.35
##  [226,]             0     24          50.60      1288.75
##  [227,]             0     31          81.15      2545.75
##  [228,]             0      1          55.20        55.20
##  [229,]             0     30          89.90      2723.15
##  [230,]             0     47          85.30      4107.25
##  [231,]             0     54         108.00      5760.65
##  [232,]             0     50          93.50      4747.50
##  [233,]             0      1          84.60        84.60
##  [234,]             0     72          20.25      1566.90
##  [235,]             0     29          25.15       702.00
##  [236,]             0      2          54.40       114.10
##  [237,]             0     10          29.60       299.05
##  [238,]             0     18          73.15      1305.95
##  [239,]             1     11          95.00      1120.30
##  [240,]             0     16          19.75       284.35
##  [241,]             0     72          86.60      6350.50
##  [242,]             0     72         109.20      7878.30
##  [243,]             0     41          74.70      3187.65
##  [244,]             1     65          94.40      6126.15
##  [245,]             1     13          54.80       731.30
##  [246,]             1      4          75.35       273.40
##  [247,]             0     41          65.00      2531.80
##  [248,]             1     15          74.40      1074.30
##  [249,]             0      1          48.55        48.55
##  [250,]             0     42          99.00      4298.45
##  [251,]             0     51          93.50      4619.55
##  [252,]             0      2          70.40       147.15
##  [253,]             1      1          40.20        40.20
##  [254,]             0     32          83.70      2633.30
##  [255,]             0     10          19.85       193.05
##  [256,]             0     67          59.55      4103.90
##  [257,]             0     61         115.10      7008.15
##  [258,]             0     50         114.35      5791.10
##  [259,]             0      2          44.60        80.55
##  [260,]             1     29          45.00      1228.65
##  [261,]             1      3          41.15       132.20
##  [262,]             1     13         106.90      1364.30
##  [263,]             1     57          89.85      4925.35
##  [264,]             0     31          49.85      1520.10
##  [265,]             0     45         113.30      5032.25
##  [266,]             0     61          88.10      5526.75
##  [267,]             0     50          24.90      1195.25
##  [268,]             1     19         105.00      2007.25
##  [269,]             0     59          19.35      1099.60
##  [270,]             0     71          24.25      1732.95
##  [271,]             1     16          94.45      1511.20
##  [272,]             0     57          59.75      3450.15
##  [273,]             0      1          24.80        24.80
##  [274,]             1     20         107.05      2172.05
##  [275,]             0      1          70.60        70.60
##  [276,]             0      5          85.40       401.10
##  [277,]             0     52         105.05      5624.85
##  [278,]             1     21          64.95      1339.80
##  [279,]             0     14          55.00       771.95
##  [280,]             0      5          50.55       244.75
##  [281,]             0      6          55.15       322.90
##  [282,]             0     10          51.20       498.25
##  [283,]             0      1          25.40        25.40
##  [284,]             0     68          54.45      3687.75
##  [285,]             0     18          95.15      1779.95
##  [286,]             0     22          76.00      1783.60
##  [287,]             0     20          44.35       927.15
##  [288,]             0      1          70.00        70.00
##  [289,]             1      8          74.50       606.55
##  [290,]             0     10          44.85       435.40
##  [291,]             1     24          76.10      1712.70
##  [292,]             0     35          61.20      2021.20
##  [293,]             0     23          86.80      1940.80
##  [294,]             1      6          89.35       567.80
##  [295,]             0     12          19.70       220.35
##  [296,]             0      1          20.25        20.25
##  [297,]             0     71          76.05      5436.45
##  [298,]             1     35         100.80      3437.50
##  [299,]             0     40          74.55      3015.75
##  [300,]             0      1          73.60        73.60
##  [301,]             0     23          64.90      1509.80
##  [302,]             1      4          95.45       396.10
##  [303,]             0      4          90.40       356.65
##  [304,]             0     68          60.30      4109.00
##  [305,]             0     38          81.85      3141.70
##  [306,]             0     52          24.80      1229.10
##  [307,]             1     32          74.90      2303.35
##  [308,]             0     29          75.55      2054.40
##  [309,]             1     38         101.15      3741.85
##  [310,]             0     48          78.75      3682.45
##  [311,]             0      1          19.25        19.25
##  [312,]             0     22          89.05      1886.25
##  [313,]             0     43         115.05      4895.10
##  [314,]             1      5          69.35       341.60
##  [315,]             0      5          80.60       415.55
##  [316,]             0     51         110.05      5686.40
##  [317,]             0     71          19.90      1355.10
##  [318,]             0     38          80.30      3058.65
##  [319,]             1     24          93.15      2231.05
##  [320,]             0     35          91.50      3236.35
##  [321,]             1     54          82.45      4350.10
##  [322,]             0     72          60.00      4264.00
##  [323,]             0      1          44.80        44.80
##  [324,]             0      9          48.60       422.30
##  [325,]             0     69          60.05      4176.70
##  [326,]             0     52         102.70      5138.10
##  [327,]             1     11          82.90       880.05
##  [328,]             1      2          70.35       139.05
##  [329,]             1     28          35.90       973.65
##  [330,]             1     17          82.65      1470.05
##  [331,]             0     35          19.85       739.35
##  [332,]             0      8          19.20       161.95
##  [333,]             0     46          94.90      4422.95
##  [334,]             0      7          73.85       511.25
##  [335,]             0      2          80.60       155.80
##  [336,]             0     68          75.80      5293.95
##  [337,]             0     43         104.60      4759.85
##  [338,]             0     68          88.15      6148.45
##  [339,]             0     36          94.80      3565.65
##  [340,]             0     63         103.40      6603.00
##  [341,]             1     32          54.65      1830.10
##  [342,]             0     71          85.75      6223.80
##  [343,]             0     66          67.45      4508.65
##  [344,]             0     63          20.50      1328.15
##  [345,]             0     41          20.25       865.00
##  [346,]             1      1          72.10        72.10
##  [347,]             0      2          90.40       168.20
##  [348,]             0     70          19.45      1303.50
##  [349,]             0     23          44.95       996.85
##  [350,]             1     64          97.00      6430.90
##  [351,]             0     37          62.80      2278.75
##  [352,]             0     17          44.60       681.40
##  [353,]             1      7          89.15       574.35
##  [354,]             0      4          84.80       371.90
##  [355,]             1     21          41.90       840.10
##  [356,]             0     10          80.25       846.00
##  [357,]             1     16          54.10       889.00
##  [358,]             0     64         105.25      6823.40
##  [359,]             1     27          30.75       805.10
##  [360,]             0     42          97.10      4016.75
##  [361,]             0      5          20.20        83.75
##  [362,]             0     41          98.80      3959.15
##  [363,]             0     58          50.30      2878.55
##  [364,]             0     47          20.55       945.70
##  [365,]             0     18          75.90      1373.05
##  [366,]             0      5          96.50       492.55
##  [367,]             0     23          59.95      1406.00
##  [368,]             0      1          19.15        19.15
##  [369,]             0     71          98.65      6962.85
##  [370,]             0     72         112.60      8126.65
##  [371,]             0     33          20.60       690.25
##  [372,]             0      2          85.65       181.50
##  [373,]             0     24          35.75       830.80
##  [374,]             0     56          99.75      5608.40
##  [375,]             0     37          96.10      3646.80
##  [376,]             0     43          85.10      3662.25
##  [377,]             0      1          25.35        25.35
##  [378,]             0     25         104.95      2566.50
##  [379,]             0     61          89.65      5308.70
##  [380,]             0     17          86.75      1410.25
##  [381,]             0     41          86.20      3339.05
##  [382,]             0      1          50.65        50.65
##  [383,]             1     72          64.80      4732.35
##  [384,]             0      1          90.85        90.85
##  [385,]             0     48         108.10      5067.45
##  [386,]             1     11          19.95       214.75
##  [387,]             1     55          85.45      4874.70
##  [388,]             0     42          54.75      2348.45
##  [389,]             0     44          90.40      4063.00
##  [390,]             0      1          44.00        44.00
##  [391,]             0     27          95.60      2595.25
##  [392,]             1     27          84.80      2309.55
##  [393,]             1      2          44.30        89.30
##  [394,]             0     19          19.90       367.55
##  [395,]             1     42          95.05      3944.50
##  [396,]             0     66          90.05      5965.95
##  [397,]             1     33         109.90      3694.70
##  [398,]             0     34          73.95      2524.45
##  [399,]             1     33          54.60      1803.70
##  [400,]             0     23          20.05       415.10
##  [401,]             0     32          19.75       624.15
##  [402,]             0     11          20.05       237.70
##  [403,]             0     69          99.45      7007.60
##  [404,]             0     68          55.90      3848.80
##  [405,]             0     20          19.70       419.40
##  [406,]             0     72          19.80      1468.75
##  [407,]             0     60          95.40      5812.00
##  [408,]             1     32          93.95      2861.45
##  [409,]             0      1          19.90        19.90
##  [410,]             0      1          19.60        19.60
##  [411,]             1      3          81.35       233.70
##  [412,]             0     46          24.45      1066.15
##  [413,]             0     29          74.95      2149.05
##  [414,]             0     51          87.35      4473.00
##  [415,]             1     48          70.65      3545.05
##  [416,]             0     16          73.25      1195.75
##  [417,]             0     70          98.70      6858.90
##  [418,]             0     40          24.80      1024.70
##  [419,]             0     22          83.30      1845.90
##  [420,]             1      1          75.30        75.30
##  [421,]             0      5          24.30       132.25
##  [422,]             0      7          69.85       515.45
##  [423,]             0     29         100.55      2830.45
##  [424,]             0     44          25.70      1110.50
##  [425,]             0     10          40.70       449.30
##  [426,]             1     55          51.65      2838.55
##  [427,]             1     52         105.10      5376.40
##  [428,]             0     10          85.95       858.60
##  [429,]             0     18          75.60      1395.05
##  [430,]             0     68          58.25      3975.70
##  [431,]             0     61          19.40      1182.55
##  [432,]             0     72          65.20      4784.45
##  [433,]             0      2          53.45       119.50
##  [434,]             0     12          45.40       518.90
##  [435,]             0     41          19.75       899.45
##  [436,]             0     26          44.45      1183.80
##  [437,]             0     36          20.85       720.05
##  [438,]             0     72         114.05      8468.20
##  [439,]             0     35          89.85      3161.20
##  [440,]             0      1          55.05        55.05
##  [441,]             0     16         112.95      1882.55
##  [442,]             1     49         101.55      5070.40
##  [443,]             0     54         114.65      6049.50
##  [444,]             0     18          64.80      1166.70
##  [445,]             0     36          80.40      2937.65
##  [446,]             0     60         105.90      6396.45
##  [447,]             0      1          69.55        69.55
##  [448,]             0     52          25.05      1270.25
##  [449,]             0      8          94.75       759.55
##  [450,]             0     72         105.50      7611.55
##  [451,]             0     64          24.70      1642.75
##  [452,]             1     22          69.75      1545.40
##  [453,]             0     60          60.20      3582.40
##  [454,]             0     28          81.05      2227.10
##  [455,]             0     61          24.40      1417.90
##  [456,]             0     24         104.15      2494.65
##  [457,]             0     28          92.90      2768.35
##  [458,]             0     30          80.80      2369.30
##  [459,]             0      2          20.00        38.00
##  [460,]             0      1          75.10        75.10
##  [461,]             0      6          19.65       100.90
##  [462,]             0     24          69.45      1614.05
##  [463,]             0      4         101.15       385.90
##  [464,]             0      7          99.80       673.25
##  [465,]             1     72         116.05      8404.90
##  [466,]             0     70          40.05      2799.75
##  [467,]             1     64         102.10      6538.45
##  [468,]             0     72          89.70      6588.95
##  [469,]             0     44          19.90       868.10
##  [470,]             0     13          55.95       734.35
##  [471,]             1     17          20.65       330.60
##  [472,]             0      1          55.00        55.00
##  [473,]             0      9          70.05       564.40
##  [474,]             0     24          53.60      1315.35
##  [475,]             0      1          74.70        74.70
##  [476,]             0     24          80.25      1861.50
##  [477,]             1     35          76.05      2747.20
##  [478,]             0      7          75.70       554.05
##  [479,]             0      5          96.10       453.40
##  [480,]             0     15          69.00       994.80
##  [481,]             0     11          19.65       225.75
##  [482,]             0     48          45.30      2145.00
##  [483,]             1     20          81.45      1671.60
##  [484,]             0     72         108.50      8003.80
##  [485,]             0      8          83.55       680.05
##  [486,]             0     72          84.50      6130.85
##  [487,]             0     15         100.15      1415.00
##  [488,]             0     72          88.60      6201.95
##  [489,]             0      1          74.35        74.35
##  [490,]             0     63         104.80      6597.25
##  [491,]             0      2          59.00       114.15
##  [492,]             0      2          74.40       139.40
##  [493,]             1     61          64.05      3902.60
##  [494,]             0      1          20.40        20.40
##  [495,]             0     22          43.75       903.60
##  [496,]             0     28          60.90      1785.65
##  [497,]             0     70          19.80      1397.65
##  [498,]             1      5          28.45       131.05
##  [499,]             0     12          99.70      1238.45
##  [500,]             0     34         116.25      3899.05
##  [501,]             1     71          80.70      5676.00
##  [502,]             0     70          65.20      4543.15
##  [503,]             0     52          84.05      4326.80
##  [504,]             0     69          79.45      5502.55
##  [505,]             1     20          94.10      1782.40
##  [506,]             0     11          78.00       851.80
##  [507,]             0      2          94.20       167.50
##  [508,]             0      6          80.50       502.85
##  [509,]             0      1          19.85        19.85
##  [510,]             1     20          94.30      1818.30
##  [511,]             0     61         106.45      6300.15
##  [512,]             1      5          74.35       334.80
##  [513,]             0     56         105.45      5916.95
##  [514,]             0     30          95.00      2852.40
##  [515,]             0     40         104.80      4131.95
##  [516,]             0     28          54.30      1546.30
##  [517,]             1      5          70.05       302.60
##  [518,]             1     27          75.20      1929.35
##  [519,]             0     12          20.05       265.45
##  [520,]             0     67         105.40      6989.45
##  [521,]             1     29          51.60      1442.00
##  [522,]             0     55          85.50      4713.40
##  [523,]             0     23          75.60      1758.60
##  [524,]             0     34         100.05      3480.00
##  [525,]             0     52          91.25      4738.30
##  [526,]             1     72         115.75      8399.15
##  [527,]             0     58          94.70      5430.35
##  [528,]             0     35          19.60       686.95
##  [529,]             1     56          99.90      5706.30
##  [530,]             0     24          21.10       490.65
##  [531,]             0     70          20.05      1360.25
##  [532,]             0      2          79.95       174.45
##  [533,]             1     68         107.15      7379.80
##  [534,]             0      1          85.00        85.00
##  [535,]             0     12          89.55      1021.75
##  [536,]             0     63          81.55      5029.05
##  [537,]             0     33          58.45      1955.40
##  [538,]             0     69          95.65      6744.20
##  [539,]             0     60          80.60      4946.70
##  [540,]             0     72         113.10      8248.50
##  [541,]             0     11          58.95       601.60
##  [542,]             0      1          19.55        19.55
##  [543,]             0     10          86.05       834.10
##  [544,]             0     13          45.55       597.00
##  [545,]             0     34          78.95      2647.20
##  [546,]             0     39          86.30      3266.00
##  [547,]             0     65         105.05      6744.25
##  [548,]             1     50         101.90      5265.50
##  [549,]             0     15          19.75       311.60
##  [550,]             0     72         110.30      7966.90
##  [551,]             0     72         115.60      8220.40
##  [552,]             0     55          19.35      1153.25
##  [553,]             0     23          25.60       514.75
##  [554,]             0     32          80.35      2596.15
##  [555,]             0     56          68.75      3808.00
##  [556,]             0      1          19.90        19.90
##  [557,]             0     38          70.60      2708.20
##  [558,]             0     11          70.20       760.05
##  [559,]             0      1          49.30        49.30
##  [560,]             0     56         107.25      6033.30
##  [561,]             0      3          23.60        89.05
##  [562,]             0      7          69.70       516.15
##  [563,]             0     59          99.50      5861.75
##  [564,]             0      7          64.30       445.95
##  [565,]             0     71          70.85      4973.40
##  [566,]             0     15         101.90      1667.25
##  [567,]             0     71          73.50      5357.75
##  [568,]             0     35         100.25      3527.60
##  [569,]             0     11          40.40       422.60
##  [570,]             0     60          19.25      1103.25
##  [571,]             1     47          59.60      2754.00
##  [572,]             0     11          64.90       697.25
##  [573,]             0     56         100.30      5614.45
##  [574,]             1     28         110.85      3204.40
##  [575,]             0     61          81.05      4747.65
##  [576,]             0     31          98.05      3082.10
##  [577,]             0      9          70.50       597.90
##  [578,]             1     35          94.55      3365.40
##  [579,]             0      2          19.65        38.80
##  [580,]             0     12          19.00       233.55
##  [581,]             0      1          75.30        75.30
##  [582,]             1      4          89.20       346.20
##  [583,]             0      1          19.00        19.00
##  [584,]             0      3          20.00        61.70
##  [585,]             1      1          85.70        85.70
##  [586,]             0     52          63.25      3342.45
##  [587,]             0      5          20.10        85.10
##  [588,]             0     72          99.15      7422.10
##  [589,]             0     71          90.40      6668.05
##  [590,]             0     72         111.90      8071.05
##  [591,]             0     46          24.90      1174.80
##  [592,]             0     63          83.50      5435.00
##  [593,]             0     30          84.30      2438.60
##  [594,]             0      1          45.60        45.60
##  [595,]             0     12          61.65       713.75
##  [596,]             0     16          54.85       916.15
##  [597,]             0      4          65.55       237.20
##  [598,]             0     51          90.35      4614.55
##  [599,]             0     65          20.40      1414.45
##  [600,]             0     16          74.55      1170.50
##  [601,]             0      2          19.95        47.70
##  [602,]             0     66          74.25      4859.25
##  [603,]             0     46         108.65      4903.20
##  [604,]             0     32         109.55      3608.00
##  [605,]             0     72          86.65      6094.25
##  [606,]             0     38          81.00      3084.90
##  [607,]             0     51          47.85      2356.75
##  [608,]             0     72         114.55      8306.05
##  [609,]             1     65         105.25      6786.40
##  [610,]             0      9          29.95       248.95
##  [611,]             0      9          65.00       663.05
##  [612,]             0     66          20.55      1357.10
##  [613,]             1     44         109.80      4860.35
##  [614,]             0     50          69.50      3418.20
##  [615,]             0     15          48.85       631.40
##  [616,]             0      8          25.25       186.30
##  [617,]             1     66         102.85      6976.75
##  [618,]             0     57          87.55      4884.85
##  [619,]             0      7          78.55       522.95
##  [620,]             1     10          34.55       362.60
##  [621,]             0     62          92.05      5755.80
##  [622,]             0     40          85.05      3355.65
##  [623,]             0     20          19.70       406.95
##  [624,]             0      7          20.00       137.60
##  [625,]             0     25          95.15      2395.70
##  [626,]             0     23          84.25      1968.10
##  [627,]             1     66         104.60      6819.45
##  [628,]             1     72         111.65      7943.45
##  [629,]             1     49          90.05      4547.25
##  [630,]             1     43         110.75      4687.90
##  [631,]             0     46          55.00      2473.95
##  [632,]             0     72          89.85      6562.90
##  [633,]             0     10          20.35       176.30
##  [634,]             0     40          54.55      2236.20
##  [635,]             0     65         105.50      6985.65
##  [636,]             0     31          99.45      3109.90
##  [637,]             0     68          70.90      4911.35
##  [638,]             1     56         104.55      5794.65
##  [639,]             0     10          85.25       855.30
##  [640,]             0     68          25.40      1620.20
##  [641,]             0     43          56.15      2499.30
##  [642,]             0      1          89.55        89.55
##  [643,]             1     49          89.85      4287.20
##  [644,]             0     15          25.25       394.85
##  [645,]             1     20          94.55      1899.65
##  [646,]             0      1          45.70        45.70
##  [647,]             0     50          69.65      3442.15
##  [648,]             1      2          89.50       161.50
##  [649,]             1     24          70.00      1732.60
##  [650,]             0      3          69.55       222.30
##  [651,]             0      1          74.60        74.60
##  [652,]             0     35          20.10       655.30
##  [653,]             0     17          24.80       475.25
##  [654,]             1      8          19.65       164.30
##  [655,]             0     10          95.10       865.10
##  [656,]             0     68          88.85      6132.70
##  [657,]             0     45          78.80      3597.50
##  [658,]             0      2          19.85        35.90
##  [659,]             0     37          20.35       697.65
##  [660,]             0      4          24.25        96.05
##  [661,]             0     10          45.25       428.70
##  [662,]             0      1          20.05        20.05
##  [663,]             0     65          69.55      4459.15
##  [664,]             0     57          19.50      1167.60
##  [665,]             0      3          74.75       238.10
##  [666,]             0      2          69.65       145.15
##  [667,]             0     49          30.20      1453.10
##  [668,]             0      4          45.65       191.05
##  [669,]             0     70          57.80      4039.30
##  [670,]             0     53          19.85      1039.45
##  [671,]             0     53          25.55      1336.10
##  [672,]             0      1          75.05        75.05
##  [673,]             0     22          24.85       493.40
##  [674,]             1     52          49.15      2550.90
##  [675,]             1     65         110.35      7246.15
##  [676,]             0     48          24.55      1203.95
##  [677,]             0      2          34.70        62.25
##  [678,]             0      3         107.95       313.60
##  [679,]             0     45          81.40      3775.85
##  [680,]             0      1          80.00        80.00
##  [681,]             0     61          73.80      4616.05
##  [682,]             0      3          64.40       195.65
##  [683,]             1     40         103.75      4188.40
##  [684,]             0      1          71.10        71.10
##  [685,]             0      1          49.90        49.90
##  [686,]             0     51          24.60      1266.40
##  [687,]             1      2          49.25        91.10
##  [688,]             0     52          30.10      1623.40
##  [689,]             0     51          83.40      4149.45
##  [690,]             0      1          20.45        20.45
##  [691,]             0     31          75.25      2344.50
##  [692,]             0     47          20.55      1013.05
##  [693,]             0      3          75.10       270.70
##  [694,]             1     22          20.05       417.00
##  [695,]             0      1          20.65        20.65
##  [696,]             0     72          85.15      6316.20
##  [697,]             0      3          50.15       168.15
##  [698,]             1     47          84.95      4018.05
##  [699,]             0     72          66.50      4811.60
##  [700,]             0     66          63.30      4189.70
##  [701,]             0     35          83.15      2848.45
##  [702,]             0     29          84.90      2516.20
##  [703,]             0      2          20.55        33.60
##  [704,]             0      4          49.25       208.45
##  [705,]             0     25          79.85      2015.35
##  [706,]             0     65          59.60      3739.80
##  [707,]             1     27         104.65      2964.00
##  [708,]             0     29          75.30      2263.40
##  [709,]             0     29          80.10      2211.80
##  [710,]             0      1          19.55        19.55
##  [711,]             0     20          81.00      1683.70
##  [712,]             0     58          24.70      1519.00
##  [713,]             0     14          86.00      1164.05
##  [714,]             0     72          25.40      1710.90
##  [715,]             0     46          89.15      4245.55
##  [716,]             0     71          58.25      4145.90
##  [717,]             0     32          85.65      2664.30
##  [718,]             0     26          50.35      1277.50
##  [719,]             1     68          80.35      5589.30
##  [720,]             0      2          20.20        34.75
##  [721,]             0     61          20.55      1305.95
##  [722,]             0      4          85.95       381.30
##  [723,]             0      3          45.35       141.50
##  [724,]             1     33          94.50      3105.55
##  [725,]             1      9          21.25       204.55
##  [726,]             0     22          26.25       605.90
##  [727,]             0      5          80.85       356.10
##  [728,]             1     30          91.70      2758.15
##  [729,]             0     65          74.20      4805.65
##  [730,]             0     45          87.25      3941.70
##  [731,]             0      5          20.35        92.75
##  [732,]             0     25          75.50      1901.05
##  [733,]             0     72          79.05      5730.70
##  [734,]             0     27          90.15      2423.40
##  [735,]             0     32          50.60      1653.45
##  [736,]             0     30         110.45      3327.05
##  [737,]             0     70         101.00      7085.50
##  [738,]             1     42          79.35      3344.10
##  [739,]             1     72          89.85      6697.35
##  [740,]             0     47          65.00      2879.90
##  [741,]             0      2          80.45       137.10
##  [742,]             0     10          98.55      1008.55
##  [743,]             0     61          24.10      1551.60
##  [744,]             0      5          44.05       202.15
##  [745,]             1     72         110.80      7882.25
##  [746,]             1     72         114.95      8196.40
##  [747,]             1      3          75.05       202.90
##  [748,]             0     48          19.25       855.10
##  [749,]             0     63          90.05      5817.00
##  [750,]             0     27          56.70      1652.95
##  [751,]             0     70          80.15      5600.15
##  [752,]             0      7          71.35       515.75
##  [753,]             0      2          90.35       190.50
##  [754,]             1     20          98.55      1842.80
##  [755,]             0     66          19.70      1253.80
##  [756,]             0      3          19.85        57.20
##  [757,]             0     15          85.90      1269.55
##  [758,]             0     72          90.35      6563.40
##  [759,]             0      1          20.80        20.80
##  [760,]             0     22          89.25      1907.85
##  [761,]             0      3          70.30       208.85
##  [762,]             0     72          66.85      4758.80
##  [763,]             0     65          19.90      1292.60
##  [764,]             0     11          35.80       363.15
##  [765,]             0     22          78.85      1600.25
##  [766,]             0     14          20.40       275.70
##  [767,]             0     41          74.25      3089.10
##  [768,]             0     17          64.80      1175.60
##  [769,]             0     11          20.45       237.30
##  [770,]             0     15          93.35      1444.65
##  [771,]             0      1          19.90        19.90
##  [772,]             0      5          88.90       454.15
##  [773,]             0     33          95.80      3036.75
##  [774,]             0     72         110.65      8065.65
##  [775,]             0      3          40.30        92.50
##  [776,]             0      2          82.00       184.65
##  [777,]             0     59         107.00      6152.30
##  [778,]             0      2          45.35        89.50
##  [779,]             0     71          73.35      5154.50
##  [780,]             0      5          44.80       220.45
##  [781,]             0     27          54.75      1510.30
##  [782,]             0      1          52.20        52.20
##  [783,]             0     63          40.60      2588.95
##  [784,]             1     46         110.00      4874.80
##  [785,]             0     72          55.30      3983.60
##  [786,]             0     34          60.85      2003.60
##  [787,]             0     24          78.40      1832.40
##  [788,]             0     72          69.65      4908.25
##  [789,]             0     60          59.85      3590.20
##  [790,]             0     68          76.90      5023.00
##  [791,]             0      8          19.85       146.60
##  [792,]             0     34          67.65      2339.30
##  [793,]             0      6          45.00       298.70
##  [794,]             0      2          64.20       143.65
##  [795,]             0     31          81.70      2548.65
##  [796,]             0     20          25.55       507.40
##  [797,]             0      1          20.00        20.00
##  [798,]             0     62          96.75      6125.40
##  [799,]             1     70          75.65      5411.40
##  [800,]             0     10          98.50      1058.25
##  [801,]             0     39          23.80       903.80
##  [802,]             0     46          64.20      3009.50
##  [803,]             0      6          85.35       489.45
##  [804,]             0     72          76.80      5468.45
##  [805,]             0     18          55.20      1058.10
##  [806,]             0     71         108.55      7616.00
##  [807,]             0     40         101.30      4113.10
##  [808,]             0      1          69.55        69.55
##  [809,]             0     58         103.25      6017.65
##  [810,]             0     70         104.00      7250.15
##  [811,]             0     42          25.25      1108.20
##  [812,]             0     34          30.40       938.65
##  [813,]             1      5          20.05        94.15
##  [814,]             0     25          84.60      2088.05
##  [815,]             0      2          86.20       178.70
##  [816,]             0     55         103.70      5656.75
##  [817,]             0     21         111.20      2317.10
##  [818,]             0     70          88.00      5986.45
##  [819,]             0     61         106.35      6751.35
##  [820,]             0     43          79.15      3566.60
##  [821,]             0     47         103.10      4889.30
##  [822,]             0      5          63.95       318.10
##  [823,]             0     62          25.80      1563.95
##  [824,]             0     16          89.45      1430.25
##  [825,]             1      7          95.60       644.35
##  [826,]             0     14          25.55       372.45
##  [827,]             0     60          90.95      5453.40
##  [828,]             0     34          44.85      1442.60
##  [829,]             0     50         108.55      5610.70
##  [830,]             0     38          25.05       963.95
##  [831,]             0     70          74.10      5222.30
##  [832,]             0     37          88.80      3340.55
##  [833,]             1      4          78.85       292.80
##  [834,]             1     60          93.25      5774.55
##  [835,]             0     62          71.40      4487.30
##  [836,]             0      1          44.40        44.40
##  [837,]             0     36          79.20      2854.95
##  [838,]             0     44          20.40       905.55
##  [839,]             1     55         100.00      5509.30
##  [840,]             0     72         105.00      7589.80
##  [841,]             0     12          19.80       229.60
##  [842,]             0     13          30.85       394.10
##  [843,]             0      1          89.90        89.90
##  [844,]             0     15          20.55       295.95
##  [845,]             0     65          84.85      5459.20
##  [846,]             0     12          33.15       444.75
##  [847,]             0     72          92.00      6782.15
##  [848,]             0     72          89.80      6510.45
##  [849,]             0     72         115.80      8476.50
##  [850,]             0     52          85.15      4461.85
##  [851,]             0      2          24.85        62.00
##  [852,]             0      5          64.35       352.65
##  [853,]             0     68          20.50      1424.90
##  [854,]             0     62         100.15      6413.65
##  [855,]             0     72          86.05      6309.65
##  [856,]             0      1          50.80        50.80
##  [857,]             0     66          89.00      5898.60
##  [858,]             0     72          64.80      4719.75
##  [859,]             0     26          19.80       457.30
##  [860,]             0     64          93.40      5822.30
##  [861,]             1     20          73.65      1463.50
##  [862,]             0      3          95.10       307.40
##  [863,]             0     22          94.65      2104.55
##  [864,]             0      4          80.60       319.15
##  [865,]             0     62          39.00      2337.45
##  [866,]             0      5          20.50       104.30
##  [867,]             0     59          85.55      5084.65
##  [868,]             0      3          26.40       121.25
##  [869,]             0     72          98.20      7015.90
##  [870,]             0     57          97.55      5598.00
##  [871,]             0     66          19.95      1269.10
##  [872,]             0     60          50.80      3027.40
##  [873,]             0     45          99.70      4634.35
##  [874,]             0      3          34.80       113.95
##  [875,]             0     15         105.10      1582.75
##  [876,]             0     51          60.15      3077.00
##  [877,]             0     60          64.75      4039.50
##  [878,]             0     33          54.65      1665.20
##  [879,]             0     10         110.10      1043.30
##  [880,]             1     26          19.30       504.20
##  [881,]             0      6          83.90       497.55
##  [882,]             0     67         111.25      7511.65
##  [883,]             0     49          35.80      1782.00
##  [884,]             0      1          20.05        20.05
##  [885,]             1      7          84.35       609.65
##  [886,]             1     27         110.50      2857.60
##  [887,]             0     37          91.20      3247.55
##  [888,]             0     63         100.55      6215.35
##  [889,]             0     31          89.30      2823.00
##  [890,]             0     50         103.85      5017.90
##  [891,]             1     32          81.10      2619.25
##  [892,]             0      1          24.60        24.60
##  [893,]             0     63          81.20      4965.10
##  [894,]             0     30          94.30      2679.70
##  [895,]             0     71         116.10      8310.55
##  [896,]             0     53         105.55      5682.25
##  [897,]             0     12          98.90      1120.95
##  [898,]             0     50          94.40      4914.90
##  [899,]             0      2          19.50        27.55
##  [900,]             0      9          98.30       923.50
##  [901,]             0     17          93.85      1625.65
##  [902,]             0     56         105.60      6068.65
##  [903,]             0     67          81.35      5398.60
##  [904,]             1      9         100.50       918.60
##  [905,]             0      4          56.40       234.85
##  [906,]             0     19          65.35      1231.85
##  [907,]             0      8          19.95       170.90
##  [908,]             0     71         111.25      7984.15
##  [909,]             1     10          72.85       688.65
##  [910,]             1     15          89.00      1288.30
##  [911,]             0     72         106.10      7848.50
##  [912,]             0     12          20.05       267.00
##  [913,]             0     72          25.20      1798.90
##  [914,]             1      1          73.55        73.55
##  [915,]             1     23          75.40      1643.55
##  [916,]             0     72          65.55      4807.45
##  [917,]             0     26          80.70      2193.00
##  [918,]             0     21         104.55      2239.40
##  [919,]             0     60          24.15      1505.90
##  [920,]             0     12          20.45       255.35
##  [921,]             0     16          75.40      1189.40
##  [922,]             0     63          79.70      4786.15
##  [923,]             1     22          81.70      1820.90
##  [924,]             0     32          76.30      2404.15
##  [925,]             1      3          79.40       205.05
##  [926,]             0     13          81.15       952.30
##  [927,]             0     68         103.75      7039.45
##  [928,]             0     30          86.45      2538.05
##  [929,]             0     16          75.10      1212.85
##  [930,]             0     33          80.60      2651.10
##  [931,]             0     72          19.30      1304.80
##  [932,]             1      4          84.60       360.10
##  [933,]             0     12          33.60       435.45
##  [934,]             1      4          83.25       308.05
##  [935,]             0      6          79.05       434.50
##  [936,]             0     65         108.05      7118.90
##  [937,]             0     15          19.90       320.45
##  [938,]             0     24          21.05       531.55
##  [939,]             0     13          30.15       382.20
##  [940,]             0     24          79.85      2001.00
##  [941,]             0     72          65.50      4919.70
##  [942,]             0     54         104.10      5645.80
##  [943,]             0      3          74.40       215.80
##  [944,]             0      4          20.50        77.60
##  [945,]             1     32          91.35      2896.55
##  [946,]             1     35          99.05      3395.80
##  [947,]             0     35          20.50       759.35
##  [948,]             1      2          44.95        85.15
##  [949,]             0      8          75.60       535.55
##  [950,]             0     22          55.10      1253.15
##  [951,]             0     15          58.95       955.15
##  [952,]             0     22          95.10      2162.60
##  [953,]             0      1          44.70        44.70
##  [954,]             0     71          25.45      1813.35
##  [955,]             0      4          56.75       245.15
##  [956,]             0     25          81.75      2028.80
##  [957,]             0     32          86.10      2723.75
##  [958,]             1      7          29.80       220.45
##  [959,]             0     17          20.50       365.80
##  [960,]             1      8          60.90       551.95
##  [961,]             1     56          73.25      4054.20
##  [962,]             0      1          45.70        45.70
##  [963,]             1      8         100.30       832.35
##  [964,]             0      7          19.25       112.30
##  [965,]             0      3          20.85        60.65
##  [966,]             0     71          77.35      5550.10
##  [967,]             0      2          96.00       174.80
##  [968,]             0      1          90.55        90.55
##  [969,]             0     49          93.85      4733.10
##  [970,]             0     58          70.10      4048.95
##  [971,]             1     44          30.35      1359.70
##  [972,]             0     59          75.95      4542.35
##  [973,]             0     71         108.05      7532.15
##  [974,]             0      1          69.90        69.90
##  [975,]             0     11          75.25       888.65
##  [976,]             1     62         103.75      6383.35
##  [977,]             0     35          54.95      1916.00
##  [978,]             0     20          19.50       413.00
##  [979,]             0     40          19.60       808.95
##  [980,]             0     39          47.85      1886.40
##  [981,]             0      1          86.60        86.60
##  [982,]             0     72          23.75      1679.25
##  [983,]             1     33          80.60      2656.50
##  [984,]             0     12          43.80       540.95
##  [985,]             0      1          19.75        19.75
##  [986,]             0     27          19.15       537.35
##  [987,]             0     34          19.60       678.80
##  [988,]             0     56          80.30      4513.65
##  [989,]             0     58          24.35      1423.85
##  [990,]             0     22          25.25       555.40
##  [991,]             0     10          26.10       225.55
##  [992,]             0     13          20.00       268.45
##  [993,]             0     35          85.30      2917.50
##  [994,]             0     34          70.00      2416.10
##  [995,]             1      4          94.30       424.45
##  [996,]             0     72          20.70      1492.10
##  [997,]             0      2          70.30       132.40
##  [998,]             0      7          95.35       660.90
##  [999,]             1     27          75.50      1893.95
drop(scale(new_telecom,center=center, scale=scale)%*%telecom_pca$rotation[,1])
##   [1] -2.015467453 -0.286167867 -1.580345244 -0.287614123 -1.294160708
##   [6] -0.494044929 -0.020111087 -1.733455753  0.688536938  0.800699638
##  [11] -1.254566657 -1.764971394  2.061385552  1.724378831  0.527494462
##  [16]  3.161504599 -0.716173101  2.952410314 -1.254731788 -0.052469384
##  [21] -1.611728253 -1.878281489 -2.175779144  0.775447113  0.410974980
##  [26] -0.507827005  1.525172980 -2.009683010  2.415256278 -0.777763717
##  [31]  2.848230035 -0.641013427 -0.300560723 -2.174952795 -1.519177173
##  [36]  2.827024440 -1.194294975  0.756572527  0.995843188 -0.372576730
##  [41] -1.361697679  1.595061949 -1.686527850  1.605413825 -0.714410979
##  [46]  1.086026186 -1.658263057 -1.134762350  1.167167537  1.311538924
##  [51]  1.264868979 -0.168370241 -0.085154857 -0.614912060  1.580551201
##  [56]  0.176758767  2.346069747  3.020282165 -1.093507929  3.124480162
##  [61]  1.531689184  1.870638938  0.648254123 -0.961557792 -0.545892972
##  [66] -1.169962034  0.875427786  0.182493361 -0.796456606 -0.750675757
##  [71] -1.698149465 -0.700659398  3.032428488 -0.313836135 -1.364614999
##  [76]  2.554954116  0.197136523 -1.322542296  0.217664019 -0.734366957
##  [81] -1.197382016 -1.296764834 -1.008206279  1.361647046 -0.806959336
##  [86] -0.448546799 -0.084717836 -0.797431545 -0.891905672 -1.031259395
##  [91]  0.227101041 -1.032457656  1.987686410  2.806811496  2.903210552
##  [96] -0.708173758  1.543929464 -2.042972026 -0.686131807  0.606006347
## [101] -2.174952795 -2.187348029  0.918938002  0.828260114  3.004049207
## [106] -1.994145410  2.910881473 -1.044980444  1.113535949 -0.182569918
## [111]  1.806754913  0.473311559  1.079176733  0.624327885  0.802448837
## [116] -0.932457938 -0.881816122 -0.368163059 -1.021001971  0.088899116
## [121]  1.959011199 -2.026197593 -1.188782751 -1.447591995 -2.083725783
## [126]  0.539725647  0.209918439 -0.010898566 -2.182389936  1.396133635
## [131] -0.488380801 -0.576201423  0.757771042 -1.922916373 -1.742382162
## [136] -0.791376856 -0.275699196 -0.376504769 -0.576670736 -1.102697315
## [141]  2.637556123 -1.031083507  2.224966267  1.824074123  0.223919674
## [146]  2.412380218 -2.127246954 -1.754341192 -0.242980107 -0.751647226
## [151] -1.073099568 -0.640030879  3.111701929  1.786414072 -2.042218618
## [156] -0.565777248 -0.137336369 -1.581914961 -0.827824399 -1.813761641
## [161] -1.105125107 -0.277685139 -1.315154533  1.019911639 -1.878916383
## [166] -0.242720302 -1.210277456  2.362522478  0.533272788 -1.742987721
## [171]  0.839076685 -0.720591805 -0.540357577  1.661339506 -1.279821564
## [176] -1.130555556 -0.408013662 -0.743385170 -0.028474511 -0.446593399
## [181] -2.013814755 -1.760125634 -0.785685539  0.143094098 -0.627242566
## [186] -2.098928694 -0.938926300 -1.945864424 -1.845639560 -0.013645536
## [191]  0.532751459 -0.763753011 -0.241701043  3.239883891 -0.529586745
## [196]  0.041504261 -1.423797011  2.505245073  3.255949403 -2.165862957
## [201]  0.513172914 -0.591288638  2.940458725 -0.665132866  0.444015173
## [206]  0.294475844  1.216941856 -1.188292177  0.191402077  2.513449429
## [211] -1.714650062 -2.091491554 -0.496532742 -1.390183335  0.214739477
## [216]  0.714439146  0.750808255  0.986205791  1.855475220 -0.869756792
## [221] -1.223800243  0.018466833 -2.174952795 -1.575912620 -1.880644639
## [226] -0.790721995  0.228193786 -1.596508547  0.398788586  1.111447309
## [231]  2.117501542  1.498031583 -1.110615378 -0.109889215 -1.259735971
## [236] -1.569694178 -1.736715414 -0.556239678 -0.172771995 -1.764254088
## [241]  2.350509329  3.159196787  0.536800409  2.494646248 -0.892448846
## [246] -0.896128512  0.189676268 -0.429468453 -1.706412954  1.275306480
## [251]  1.483814874 -1.300333090 -1.602638415  0.317688173 -1.925680891
## [256]  1.147868075  2.752892848  2.138312705 -1.738525078 -0.543376534
## [261] -1.515062327  0.136554351  1.891387507 -0.576583362  1.787988537
## [266]  1.886173788 -0.642898886  0.428243968 -0.555691572 -0.019705730
## [271]  0.045191278  0.734348784 -2.098928694  0.531953653 -1.341993078
## [276] -0.915016951  1.984786439 -0.369501616 -1.096447796 -1.526109774
## [281] -1.406045462 -1.328385636 -2.089012507  0.967514972 -0.061965617
## [286] -0.280762554 -1.087855913 -1.351909265 -0.722508773 -1.449667016
## [291] -0.012310872 -0.156304632 -0.037168857 -0.538131197 -1.874672271
## [296] -2.174126447  1.892157482  1.137964837  0.461889938 -1.292412142
## [301] -0.517387135 -0.534272919 -0.869454569  1.184296677  0.571289095
## [306] -0.589184662  0.321175896 -0.050346927  1.299967751  0.905048451
## [311] -2.190653425 -0.039180670  1.731201079 -0.951062247 -0.988780961
## [316]  2.060995141 -0.199582997  0.522109306  0.414408076  0.687022178
## [321]  1.536586078  1.315341185 -1.768389124 -1.415338168  1.222586093
## [326]  1.805900140 -0.438710303 -1.061712015 -0.787641432 -0.135536917
## [331] -1.198343873 -1.990778442  1.335829067 -1.025166682 -1.132206039
## [336]  1.778571815  1.522412449  2.226159230  0.858588810  2.491325846
## [341] -0.144465070  2.277300407  1.370391266 -0.379837665 -1.018866996
## [346] -1.075427800 -0.969489948 -0.244584145 -0.989634656  2.602197147
## [351] -0.010310742 -1.223173899 -0.516709345 -0.955977575 -0.888255721
## [356] -0.756135568 -0.789894582  2.607862820 -0.942772675  1.163010501
## [361] -2.065476607  1.151186059  0.438417864 -0.854009680 -0.492185858
## [366] -0.708337001 -0.627774818 -2.192306123  2.700440177  3.286207534
## [371] -1.245912508 -1.042774548 -1.164255026  1.985072659  0.925935526
## [376]  0.888440164 -2.089838856  0.483999792  1.848300681 -0.328025642
## [381]  0.767308022 -1.671706299  1.770465319 -1.007321763  1.782055683
## [386] -1.653232760  1.759745750 -0.006995568  1.113139875 -1.781610707
## [391]  0.386039297  0.369844689 -1.499091860 -1.669436800  1.350609046
## [396]  2.158696031  1.314538651  0.173450140 -0.130133918 -1.562150792
## [401] -1.301600987 -1.886748566  2.680816993  1.037622041 -1.634917983
## [406] -0.145573011  2.064404873  0.791862939 -2.179910889 -2.184868983
## [411] -0.832954966 -0.778633681 -0.032724793  1.341582038  0.975572007
## [416] -0.632027926  2.648422726 -0.921588574 -0.144214218 -1.022541469
## [421] -1.984879235 -1.088903843  0.579968278 -0.791065474 -1.513035429
## [426]  0.622222000  2.155542216 -0.659936889 -0.490696660  1.112469866
## [431] -0.485346062  1.550248609 -1.583558920 -1.371043561 -1.017025873
## [436] -0.875376170 -1.164910240  3.408500081  0.638502621 -1.598987594
## [441]  0.211180231  1.941101101  2.308994549 -0.732085263  0.443198603
## [446]  2.403876406 -1.359346405 -0.573228064 -0.591232088  3.021994943
## [451] -0.197906966 -0.209341868  0.848218582  0.066115975 -0.336113247
## [456]  0.427460789  0.415018801  0.148720263 -2.150278386 -1.267621674
## [461] -2.046673375 -0.390588782 -0.686440899 -0.556957327  3.664449559
## [466]  0.522505972  2.716104695  2.469786466 -0.955326849 -1.114668310
## [471] -1.471717864 -1.599813943 -1.025952606 -0.734317916 -1.274232466
## [476] -0.143678059  0.536500814 -0.982752463 -0.726151046 -0.781912460
## [481] -1.896698650 -0.082609785 -0.028423837  3.184114370 -0.796080886
## [486]  2.252905439 -0.154616411  2.340036838 -1.280016908  2.512396435
## [491] -1.494985556 -1.237622292  1.267859891 -2.171647400 -1.058855892
## [496] -0.388707308 -0.211680600 -1.676064236 -0.281294057  1.257730880
## [501]  2.278696143  1.434933438  1.268504013  1.920925370  0.209019199
## [506] -0.768218171 -0.907988452 -0.942389187 -2.180737238  0.222646044
## [511]  2.407741051 -0.871838925  2.166835286  0.518969956  1.275796804
## [516] -0.565077168 -0.950971276  0.104039221 -1.855949878  2.726633388
## [521] -0.374523696  1.472148386 -0.271709891  0.873523356  1.504387949
## [526]  3.657915782  1.897145736 -1.217553028  2.257587627 -1.500482593
## [531] -0.218434082 -1.137368632  3.132456689 -1.104004587 -0.508759846
## [536]  1.681474070 -0.265534027  2.542959902  1.573912241  3.329555277
## [541] -1.149886328 -2.185695331 -0.665396450 -1.323252191  0.290128469
## [546]  0.702260442  2.604507411  2.025966641 -1.779151384  3.202674133
## [551]  3.362025767 -0.631283339 -1.443220224  0.252550667  0.961174074
## [556] -2.179910889  0.263281260 -0.921399911 -1.694017720  2.229702111
## [561] -2.054286986 -1.091137141  2.122587928 -1.199117557  1.673845329
## [566] -0.053270584  1.827997486  0.913308574 -1.502850478 -0.533484371
## [571]  0.544662525 -1.025617080  1.995752636  1.074332370  1.546446407
## [576]  0.657681147 -1.008960174  1.015632917 -2.155730345 -1.882222441
## [581] -1.264316279 -0.650186458 -2.194785170 -2.120650619 -0.850660892
## [586]  0.646164920 -2.066710087  2.864111448  2.481246350  3.258766168
## [591] -0.739914165  1.830504634  0.225588535 -1.755167541 -1.050844002
## [596] -1.011641489 -1.307500380  1.431220027 -0.310959295 -0.618218890
## [601] -2.148285852  1.582172879  1.697947741  1.019238499  2.277235189
## [606]  0.541065110  0.088344264  3.369738816  2.861716043 -1.768292598
## [611] -1.079432495 -0.302328719  1.900456036  0.724000688 -1.214170222
## [616] -1.885499395  2.900554160  1.600556406 -0.945466070 -1.396189849
## [621]  2.039311129  0.730658097 -1.638517480 -2.007603845  0.275487690
## [626] -0.070682533  2.883492436  3.459590282  1.603114530  1.843248199
## [631]  0.124450836  2.464690667 -1.922404657 -0.088247863  2.681607106
## [636]  0.688451585  1.588390422  2.358637105 -0.672257476 -0.101957181
## [641]  0.082126335 -1.028806835  1.524682283 -1.665774215  0.250225114
## [646] -1.753514843  0.733360701 -0.744266292 -0.105608419 -1.269632476
## [651] -1.275885164 -1.218584626 -1.604284883 -1.741017171 -0.509481193
## [656]  2.232972153  0.812972782 -2.153321210 -1.156729662 -2.018932848
## [661] -1.445108950 -2.177431842  1.367403811 -0.579147415 -1.180627555
## [666] -1.313089719 -0.505065310 -1.643976554  1.169102046 -0.701617260
## [671] -0.523295116 -1.268448023 -1.484346965  0.430135923  3.077450325
## [676] -0.691618253 -1.904570742 -0.619702252  0.906755103 -1.186639480
## [681]  1.390674210 -1.360962414  1.516842469 -1.333729588 -1.684101533
## [686] -0.604423912 -1.418194032 -0.389125464  1.183898927 -2.170821051
## [691]  0.074205758 -0.834537702 -1.165519115 -1.342602374 -2.167515655
## [696]  2.317047742 -1.600302648  1.321749700  1.579207336  1.210790517
## [701]  0.439287844  0.234990959 -2.142619673 -1.580489627 -0.082916959
## [706]  0.997861324  0.881378370  0.006018899  0.069042241 -2.185695331
## [711] -0.274007379 -0.370339377 -0.479711592  0.015368512  1.191172140
## [716]  1.230004587  0.358314608 -0.752482592  2.179619376 -2.147970441
## [721] -0.430995578 -0.934586341 -1.685949334  0.894142747 -1.680623950
## [726] -1.429088383 -1.001909455  0.679910616  1.543088643  1.049696523
## [731] -2.060438882 -0.186597645  2.048719231  0.247858324 -0.503075603
## [736]  0.907073946  2.751283546  0.922089225  2.745337154  0.426971904
## [741] -1.140048192 -0.411986845 -0.302329766 -1.643972230  3.428094186
## [746]  3.586307177 -0.944158278 -0.878537118  2.047305030 -0.518047766
## [751]  1.983285330 -1.064460315 -0.963854549  0.298740306 -0.345996608
## [756] -2.124387321 -0.428057904  2.472954157 -2.165036608 -0.029688187
## [761] -1.261342692  1.569625251 -0.354307039 -1.594732604 -0.287494106
## [766] -1.801751759  0.501000967 -0.752287842 -1.880369068 -0.256461578
## [771] -2.179910889 -0.842846817  0.653585961  3.236907612 -1.782117234
## [776] -1.101132029  2.328374615 -1.723759091  1.766798933 -1.626503007
## [781] -0.590954027 -1.646089483  0.311061105  1.953432764  1.157955043
## [786] -0.189852042 -0.182131386  1.658299685  0.844790437  1.718097422
## [791] -1.984661766  0.017621739 -1.577856377 -1.402019743  0.237963047
## [796] -1.514484261 -2.178258191  2.222486439  2.097419072 -0.398429662
## [801] -0.995556301  0.428675364 -0.867509713  1.936363311 -0.919366763
## [806]  3.050031277  1.213514445 -1.359346405  2.205777418  2.847600120
## [811] -0.844588905 -0.992189274 -1.823130668  0.015231636 -1.034653249
## [816]  2.040415272  0.422277993  2.222438148  2.536566506  0.764170916
## [821]  1.626584603 -1.287315744 -0.248379102 -0.301176802 -0.391736998
## [826] -1.690154773  1.888469307 -0.611852042  1.991976537 -0.980644345
## [831]  1.775803697  0.718857287 -0.833687139  2.260440877  1.337255339
## [836] -1.774999915  0.399803256 -0.936380515  2.179479803  3.007587734
## [841] -1.870374160 -1.620610449 -1.023022392 -1.770685763  1.904973786
## [846] -1.591395342  2.562990804  2.448714628  3.439316005  1.325410808
## [851] -2.064585965 -1.270831634 -0.237987106  2.361032923  2.329768106
## [856] -1.669227253  2.122174298  1.525047644 -1.485682414  2.126009898
## [861] -0.215244250 -0.830151303  0.114865431 -1.039427478  0.189592082
## [866] -2.054663910  1.671397530 -1.999511429  2.731246468  1.969118266
## [871] -0.337513664  0.535123171  1.452114263 -1.865223934 -0.025739745
## [876]  0.496305932  1.054255883 -0.411139432 -0.214392747 -1.238466984
## [881] -0.888712772  2.972601376 -0.319042954 -2.177431842 -0.584445282
## [886]  0.945607898  0.730940347  2.332972033  0.440689837  1.744270485
## [891]  0.513182458 -2.102234090  1.657301836  0.457673081  3.373432813
## [896]  2.032276355 -0.328255504  1.561043715 -2.161418582 -0.463411359
## [901] -0.150461184  2.213129897  1.876172251 -0.187329921 -1.456756243
## [906] -0.681542804 -1.976012455  3.200311644 -0.680013377 -0.130524791
## [911]  3.100243750 -1.855501748  0.037563168 -1.051463681 -0.066445476
## [916]  1.562581534  0.005022434  0.291831878 -0.337506198 -1.852374807
## [921] -0.598952410  1.581207693  0.064352107  0.131277009 -0.872901977
## [926] -0.642461298  2.737072439  0.289252548 -0.597043994  0.295272782
## [931] -0.201092547 -0.720861909 -1.586777085 -0.757831523 -0.985695182
## [936]  2.761538392 -1.774157026 -1.489469632 -1.635417436 -0.109841490
## [941]  1.594222937  2.020968881 -1.192758099 -2.085159026  0.759792476
## [946]  1.097492431 -1.182006938 -1.489737082 -0.966949186 -0.773495578
## [951] -0.956566434  0.138955666 -1.770041822  0.023024650 -1.448095094
## [956] -0.048176408  0.382809605 -1.582744705 -1.705751462 -0.959129446
## [961]  1.347199679 -1.753514843 -0.238289481 -2.027096882 -2.107152008
## [966]  1.946124762 -0.876649752 -1.012279856  1.476775848  1.098309169
## [971] -0.401736841  1.358726322  3.017669951 -1.353561963 -0.802218360
## [976]  2.652503815 -0.288206298 -1.640015899 -1.068402284 -0.320950109
## [981] -1.077561421 -0.020574489  0.538608819 -1.390649128 -2.182389936
## [986] -1.450317558 -1.242685039  1.352736248 -0.403532037 -1.459926614
## [991] -1.814797974 -1.833118709  0.494162723  0.077984841 -0.544750016
## [996] -0.124208071 -1.306221341 -0.632786400  0.098675866
predict(telecom_pca)[,1]
##   [1] -2.015467453 -0.286167867 -1.580345244 -0.287614123 -1.294160708
##   [6] -0.494044929 -0.020111087 -1.733455753  0.688536938  0.800699638
##  [11] -1.254566657 -1.764971394  2.061385552  1.724378831  0.527494462
##  [16]  3.161504599 -0.716173101  2.952410314 -1.254731788 -0.052469384
##  [21] -1.611728253 -1.878281489 -2.175779144  0.775447113  0.410974980
##  [26] -0.507827005  1.525172980 -2.009683010  2.415256278 -0.777763717
##  [31]  2.848230035 -0.641013427 -0.300560723 -2.174952795 -1.519177173
##  [36]  2.827024440 -1.194294975  0.756572527  0.995843188 -0.372576730
##  [41] -1.361697679  1.595061949 -1.686527850  1.605413825 -0.714410979
##  [46]  1.086026186 -1.658263057 -1.134762350  1.167167537  1.311538924
##  [51]  1.264868979 -0.168370241 -0.085154857 -0.614912060  1.580551201
##  [56]  0.176758767  2.346069747  3.020282165 -1.093507929  3.124480162
##  [61]  1.531689184  1.870638938  0.648254123 -0.961557792 -0.545892972
##  [66] -1.169962034  0.875427786  0.182493361 -0.796456606 -0.750675757
##  [71] -1.698149465 -0.700659398  3.032428488 -0.313836135 -1.364614999
##  [76]  2.554954116  0.197136523 -1.322542296  0.217664019 -0.734366957
##  [81] -1.197382016 -1.296764834 -1.008206279  1.361647046 -0.806959336
##  [86] -0.448546799 -0.084717836 -0.797431545 -0.891905672 -1.031259395
##  [91]  0.227101041 -1.032457656  1.987686410  2.806811496  2.903210552
##  [96] -0.708173758  1.543929464 -2.042972026 -0.686131807  0.606006347
## [101] -2.174952795 -2.187348029  0.918938002  0.828260114  3.004049207
## [106] -1.994145410  2.910881473 -1.044980444  1.113535949 -0.182569918
## [111]  1.806754913  0.473311559  1.079176733  0.624327885  0.802448837
## [116] -0.932457938 -0.881816122 -0.368163059 -1.021001971  0.088899116
## [121]  1.959011199 -2.026197593 -1.188782751 -1.447591995 -2.083725783
## [126]  0.539725647  0.209918439 -0.010898566 -2.182389936  1.396133635
## [131] -0.488380801 -0.576201423  0.757771042 -1.922916373 -1.742382162
## [136] -0.791376856 -0.275699196 -0.376504769 -0.576670736 -1.102697315
## [141]  2.637556123 -1.031083507  2.224966267  1.824074123  0.223919674
## [146]  2.412380218 -2.127246954 -1.754341192 -0.242980107 -0.751647226
## [151] -1.073099568 -0.640030879  3.111701929  1.786414072 -2.042218618
## [156] -0.565777248 -0.137336369 -1.581914961 -0.827824399 -1.813761641
## [161] -1.105125107 -0.277685139 -1.315154533  1.019911639 -1.878916383
## [166] -0.242720302 -1.210277456  2.362522478  0.533272788 -1.742987721
## [171]  0.839076685 -0.720591805 -0.540357577  1.661339506 -1.279821564
## [176] -1.130555556 -0.408013662 -0.743385170 -0.028474511 -0.446593399
## [181] -2.013814755 -1.760125634 -0.785685539  0.143094098 -0.627242566
## [186] -2.098928694 -0.938926300 -1.945864424 -1.845639560 -0.013645536
## [191]  0.532751459 -0.763753011 -0.241701043  3.239883891 -0.529586745
## [196]  0.041504261 -1.423797011  2.505245073  3.255949403 -2.165862957
## [201]  0.513172914 -0.591288638  2.940458725 -0.665132866  0.444015173
## [206]  0.294475844  1.216941856 -1.188292177  0.191402077  2.513449429
## [211] -1.714650062 -2.091491554 -0.496532742 -1.390183335  0.214739477
## [216]  0.714439146  0.750808255  0.986205791  1.855475220 -0.869756792
## [221] -1.223800243  0.018466833 -2.174952795 -1.575912620 -1.880644639
## [226] -0.790721995  0.228193786 -1.596508547  0.398788586  1.111447309
## [231]  2.117501542  1.498031583 -1.110615378 -0.109889215 -1.259735971
## [236] -1.569694178 -1.736715414 -0.556239678 -0.172771995 -1.764254088
## [241]  2.350509329  3.159196787  0.536800409  2.494646248 -0.892448846
## [246] -0.896128512  0.189676268 -0.429468453 -1.706412954  1.275306480
## [251]  1.483814874 -1.300333090 -1.602638415  0.317688173 -1.925680891
## [256]  1.147868075  2.752892848  2.138312705 -1.738525078 -0.543376534
## [261] -1.515062327  0.136554351  1.891387507 -0.576583362  1.787988537
## [266]  1.886173788 -0.642898886  0.428243968 -0.555691572 -0.019705730
## [271]  0.045191278  0.734348784 -2.098928694  0.531953653 -1.341993078
## [276] -0.915016951  1.984786439 -0.369501616 -1.096447796 -1.526109774
## [281] -1.406045462 -1.328385636 -2.089012507  0.967514972 -0.061965617
## [286] -0.280762554 -1.087855913 -1.351909265 -0.722508773 -1.449667016
## [291] -0.012310872 -0.156304632 -0.037168857 -0.538131197 -1.874672271
## [296] -2.174126447  1.892157482  1.137964837  0.461889938 -1.292412142
## [301] -0.517387135 -0.534272919 -0.869454569  1.184296677  0.571289095
## [306] -0.589184662  0.321175896 -0.050346927  1.299967751  0.905048451
## [311] -2.190653425 -0.039180670  1.731201079 -0.951062247 -0.988780961
## [316]  2.060995141 -0.199582997  0.522109306  0.414408076  0.687022178
## [321]  1.536586078  1.315341185 -1.768389124 -1.415338168  1.222586093
## [326]  1.805900140 -0.438710303 -1.061712015 -0.787641432 -0.135536917
## [331] -1.198343873 -1.990778442  1.335829067 -1.025166682 -1.132206039
## [336]  1.778571815  1.522412449  2.226159230  0.858588810  2.491325846
## [341] -0.144465070  2.277300407  1.370391266 -0.379837665 -1.018866996
## [346] -1.075427800 -0.969489948 -0.244584145 -0.989634656  2.602197147
## [351] -0.010310742 -1.223173899 -0.516709345 -0.955977575 -0.888255721
## [356] -0.756135568 -0.789894582  2.607862820 -0.942772675  1.163010501
## [361] -2.065476607  1.151186059  0.438417864 -0.854009680 -0.492185858
## [366] -0.708337001 -0.627774818 -2.192306123  2.700440177  3.286207534
## [371] -1.245912508 -1.042774548 -1.164255026  1.985072659  0.925935526
## [376]  0.888440164 -2.089838856  0.483999792  1.848300681 -0.328025642
## [381]  0.767308022 -1.671706299  1.770465319 -1.007321763  1.782055683
## [386] -1.653232760  1.759745750 -0.006995568  1.113139875 -1.781610707
## [391]  0.386039297  0.369844689 -1.499091860 -1.669436800  1.350609046
## [396]  2.158696031  1.314538651  0.173450140 -0.130133918 -1.562150792
## [401] -1.301600987 -1.886748566  2.680816993  1.037622041 -1.634917983
## [406] -0.145573011  2.064404873  0.791862939 -2.179910889 -2.184868983
## [411] -0.832954966 -0.778633681 -0.032724793  1.341582038  0.975572007
## [416] -0.632027926  2.648422726 -0.921588574 -0.144214218 -1.022541469
## [421] -1.984879235 -1.088903843  0.579968278 -0.791065474 -1.513035429
## [426]  0.622222000  2.155542216 -0.659936889 -0.490696660  1.112469866
## [431] -0.485346062  1.550248609 -1.583558920 -1.371043561 -1.017025873
## [436] -0.875376170 -1.164910240  3.408500081  0.638502621 -1.598987594
## [441]  0.211180231  1.941101101  2.308994549 -0.732085263  0.443198603
## [446]  2.403876406 -1.359346405 -0.573228064 -0.591232088  3.021994943
## [451] -0.197906966 -0.209341868  0.848218582  0.066115975 -0.336113247
## [456]  0.427460789  0.415018801  0.148720263 -2.150278386 -1.267621674
## [461] -2.046673375 -0.390588782 -0.686440899 -0.556957327  3.664449559
## [466]  0.522505972  2.716104695  2.469786466 -0.955326849 -1.114668310
## [471] -1.471717864 -1.599813943 -1.025952606 -0.734317916 -1.274232466
## [476] -0.143678059  0.536500814 -0.982752463 -0.726151046 -0.781912460
## [481] -1.896698650 -0.082609785 -0.028423837  3.184114370 -0.796080886
## [486]  2.252905439 -0.154616411  2.340036838 -1.280016908  2.512396435
## [491] -1.494985556 -1.237622292  1.267859891 -2.171647400 -1.058855892
## [496] -0.388707308 -0.211680600 -1.676064236 -0.281294057  1.257730880
## [501]  2.278696143  1.434933438  1.268504013  1.920925370  0.209019199
## [506] -0.768218171 -0.907988452 -0.942389187 -2.180737238  0.222646044
## [511]  2.407741051 -0.871838925  2.166835286  0.518969956  1.275796804
## [516] -0.565077168 -0.950971276  0.104039221 -1.855949878  2.726633388
## [521] -0.374523696  1.472148386 -0.271709891  0.873523356  1.504387949
## [526]  3.657915782  1.897145736 -1.217553028  2.257587627 -1.500482593
## [531] -0.218434082 -1.137368632  3.132456689 -1.104004587 -0.508759846
## [536]  1.681474070 -0.265534027  2.542959902  1.573912241  3.329555277
## [541] -1.149886328 -2.185695331 -0.665396450 -1.323252191  0.290128469
## [546]  0.702260442  2.604507411  2.025966641 -1.779151384  3.202674133
## [551]  3.362025767 -0.631283339 -1.443220224  0.252550667  0.961174074
## [556] -2.179910889  0.263281260 -0.921399911 -1.694017720  2.229702111
## [561] -2.054286986 -1.091137141  2.122587928 -1.199117557  1.673845329
## [566] -0.053270584  1.827997486  0.913308574 -1.502850478 -0.533484371
## [571]  0.544662525 -1.025617080  1.995752636  1.074332370  1.546446407
## [576]  0.657681147 -1.008960174  1.015632917 -2.155730345 -1.882222441
## [581] -1.264316279 -0.650186458 -2.194785170 -2.120650619 -0.850660892
## [586]  0.646164920 -2.066710087  2.864111448  2.481246350  3.258766168
## [591] -0.739914165  1.830504634  0.225588535 -1.755167541 -1.050844002
## [596] -1.011641489 -1.307500380  1.431220027 -0.310959295 -0.618218890
## [601] -2.148285852  1.582172879  1.697947741  1.019238499  2.277235189
## [606]  0.541065110  0.088344264  3.369738816  2.861716043 -1.768292598
## [611] -1.079432495 -0.302328719  1.900456036  0.724000688 -1.214170222
## [616] -1.885499395  2.900554160  1.600556406 -0.945466070 -1.396189849
## [621]  2.039311129  0.730658097 -1.638517480 -2.007603845  0.275487690
## [626] -0.070682533  2.883492436  3.459590282  1.603114530  1.843248199
## [631]  0.124450836  2.464690667 -1.922404657 -0.088247863  2.681607106
## [636]  0.688451585  1.588390422  2.358637105 -0.672257476 -0.101957181
## [641]  0.082126335 -1.028806835  1.524682283 -1.665774215  0.250225114
## [646] -1.753514843  0.733360701 -0.744266292 -0.105608419 -1.269632476
## [651] -1.275885164 -1.218584626 -1.604284883 -1.741017171 -0.509481193
## [656]  2.232972153  0.812972782 -2.153321210 -1.156729662 -2.018932848
## [661] -1.445108950 -2.177431842  1.367403811 -0.579147415 -1.180627555
## [666] -1.313089719 -0.505065310 -1.643976554  1.169102046 -0.701617260
## [671] -0.523295116 -1.268448023 -1.484346965  0.430135923  3.077450325
## [676] -0.691618253 -1.904570742 -0.619702252  0.906755103 -1.186639480
## [681]  1.390674210 -1.360962414  1.516842469 -1.333729588 -1.684101533
## [686] -0.604423912 -1.418194032 -0.389125464  1.183898927 -2.170821051
## [691]  0.074205758 -0.834537702 -1.165519115 -1.342602374 -2.167515655
## [696]  2.317047742 -1.600302648  1.321749700  1.579207336  1.210790517
## [701]  0.439287844  0.234990959 -2.142619673 -1.580489627 -0.082916959
## [706]  0.997861324  0.881378370  0.006018899  0.069042241 -2.185695331
## [711] -0.274007379 -0.370339377 -0.479711592  0.015368512  1.191172140
## [716]  1.230004587  0.358314608 -0.752482592  2.179619376 -2.147970441
## [721] -0.430995578 -0.934586341 -1.685949334  0.894142747 -1.680623950
## [726] -1.429088383 -1.001909455  0.679910616  1.543088643  1.049696523
## [731] -2.060438882 -0.186597645  2.048719231  0.247858324 -0.503075603
## [736]  0.907073946  2.751283546  0.922089225  2.745337154  0.426971904
## [741] -1.140048192 -0.411986845 -0.302329766 -1.643972230  3.428094186
## [746]  3.586307177 -0.944158278 -0.878537118  2.047305030 -0.518047766
## [751]  1.983285330 -1.064460315 -0.963854549  0.298740306 -0.345996608
## [756] -2.124387321 -0.428057904  2.472954157 -2.165036608 -0.029688187
## [761] -1.261342692  1.569625251 -0.354307039 -1.594732604 -0.287494106
## [766] -1.801751759  0.501000967 -0.752287842 -1.880369068 -0.256461578
## [771] -2.179910889 -0.842846817  0.653585961  3.236907612 -1.782117234
## [776] -1.101132029  2.328374615 -1.723759091  1.766798933 -1.626503007
## [781] -0.590954027 -1.646089483  0.311061105  1.953432764  1.157955043
## [786] -0.189852042 -0.182131386  1.658299685  0.844790437  1.718097422
## [791] -1.984661766  0.017621739 -1.577856377 -1.402019743  0.237963047
## [796] -1.514484261 -2.178258191  2.222486439  2.097419072 -0.398429662
## [801] -0.995556301  0.428675364 -0.867509713  1.936363311 -0.919366763
## [806]  3.050031277  1.213514445 -1.359346405  2.205777418  2.847600120
## [811] -0.844588905 -0.992189274 -1.823130668  0.015231636 -1.034653249
## [816]  2.040415272  0.422277993  2.222438148  2.536566506  0.764170916
## [821]  1.626584603 -1.287315744 -0.248379102 -0.301176802 -0.391736998
## [826] -1.690154773  1.888469307 -0.611852042  1.991976537 -0.980644345
## [831]  1.775803697  0.718857287 -0.833687139  2.260440877  1.337255339
## [836] -1.774999915  0.399803256 -0.936380515  2.179479803  3.007587734
## [841] -1.870374160 -1.620610449 -1.023022392 -1.770685763  1.904973786
## [846] -1.591395342  2.562990804  2.448714628  3.439316005  1.325410808
## [851] -2.064585965 -1.270831634 -0.237987106  2.361032923  2.329768106
## [856] -1.669227253  2.122174298  1.525047644 -1.485682414  2.126009898
## [861] -0.215244250 -0.830151303  0.114865431 -1.039427478  0.189592082
## [866] -2.054663910  1.671397530 -1.999511429  2.731246468  1.969118266
## [871] -0.337513664  0.535123171  1.452114263 -1.865223934 -0.025739745
## [876]  0.496305932  1.054255883 -0.411139432 -0.214392747 -1.238466984
## [881] -0.888712772  2.972601376 -0.319042954 -2.177431842 -0.584445282
## [886]  0.945607898  0.730940347  2.332972033  0.440689837  1.744270485
## [891]  0.513182458 -2.102234090  1.657301836  0.457673081  3.373432813
## [896]  2.032276355 -0.328255504  1.561043715 -2.161418582 -0.463411359
## [901] -0.150461184  2.213129897  1.876172251 -0.187329921 -1.456756243
## [906] -0.681542804 -1.976012455  3.200311644 -0.680013377 -0.130524791
## [911]  3.100243750 -1.855501748  0.037563168 -1.051463681 -0.066445476
## [916]  1.562581534  0.005022434  0.291831878 -0.337506198 -1.852374807
## [921] -0.598952410  1.581207693  0.064352107  0.131277009 -0.872901977
## [926] -0.642461298  2.737072439  0.289252548 -0.597043994  0.295272782
## [931] -0.201092547 -0.720861909 -1.586777085 -0.757831523 -0.985695182
## [936]  2.761538392 -1.774157026 -1.489469632 -1.635417436 -0.109841490
## [941]  1.594222937  2.020968881 -1.192758099 -2.085159026  0.759792476
## [946]  1.097492431 -1.182006938 -1.489737082 -0.966949186 -0.773495578
## [951] -0.956566434  0.138955666 -1.770041822  0.023024650 -1.448095094
## [956] -0.048176408  0.382809605 -1.582744705 -1.705751462 -0.959129446
## [961]  1.347199679 -1.753514843 -0.238289481 -2.027096882 -2.107152008
## [966]  1.946124762 -0.876649752 -1.012279856  1.476775848  1.098309169
## [971] -0.401736841  1.358726322  3.017669951 -1.353561963 -0.802218360
## [976]  2.652503815 -0.288206298 -1.640015899 -1.068402284 -0.320950109
## [981] -1.077561421 -0.020574489  0.538608819 -1.390649128 -2.182389936
## [986] -1.450317558 -1.242685039  1.352736248 -0.403532037 -1.459926614
## [991] -1.814797974 -1.833118709  0.494162723  0.077984841 -0.544750016
## [996] -0.124208071 -1.306221341 -0.632786400  0.098675866
#The aboved two gives us the same thing. predict is a good function to know.
telecom$Churn <- as.factor(telecom$Churn)
out <- sapply(1:4, function(i){plot(telecom$Churn,telecom_pca$x[,i],xlab=paste("PC",i,sep=""),ylab="Churn")})

pairs(telecom_pca$x[,1:4], ylim = c(-6,4),xlim = c(-6,4),panel=function(x,y,...){text(x,y,telecom$Churn)})

# Better Ways to Visualize

library(factoextra)
## Loading required package: ggplot2
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa

library(FactoMineR)
library(ggfortify)
library(psych)
## 
## Attaching package: 'psych'
## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha
## The following object is masked from 'package:car':
## 
##     logit
library(corrplot)
## corrplot 0.92 loaded
library(devtools)
## Loading required package: usethis
# Correlation
pairs.panels(telecom[,-1],
             gap = 0,
             bg = c("red", "blue")[telecom$Churn],
             pch=21)

pairs.panels(telecom_pca$x,
             gap=0,
             bg = c("red", "blue")[telecom$Churn],
             pch=21)

fviz_eig(telecom_pca, addlabels = TRUE)

fviz_pca_var(telecom_pca,col.var = "cos2",
             gradient.cols = c("#FFCC00", "#CC9933", "#660033", "#330033"),
             repel = TRUE)

fviz_pca_ind(telecom_pca, col.ind = "cos2", 
                  gradient.cols = c("#FFCC00", "#CC9933", "#660033", "#330033"), 
                  repel = TRUE)

biplot(telecom_pca)

autoplot(telecom_pca,
         data = telecom[,-1],
         loadings = TRUE,
         labels = telecom$Churn)

# Different PCA Method. 
res.pca <- PCA(telecom[,-1], graph = FALSE)
print(res.pca)
## **Results for the Principal Component Analysis (PCA)**
## The analysis was performed on 999 individuals, described by 4 variables
## *The results are available in the following objects:
## 
##    name               description                          
## 1  "$eig"             "eigenvalues"                        
## 2  "$var"             "results for the variables"          
## 3  "$var$coord"       "coord. for the variables"           
## 4  "$var$cor"         "correlations variables - dimensions"
## 5  "$var$cos2"        "cos2 for the variables"             
## 6  "$var$contrib"     "contributions of the variables"     
## 7  "$ind"             "results for the individuals"        
## 8  "$ind$coord"       "coord. for the individuals"         
## 9  "$ind$cos2"        "cos2 for the individuals"           
## 10 "$ind$contrib"     "contributions of the individuals"   
## 11 "$call"            "summary statistics"                 
## 12 "$call$centre"     "mean of the variables"              
## 13 "$call$ecart.type" "standard error of the variables"    
## 14 "$call$row.w"      "weights for the individuals"        
## 15 "$call$col.w"      "weights for the variables"
# Visualize and Interpret PCA using these functions 

#get_eigenvalue(res.pca): Extract the eigenvalues/variances of principal components
#fviz_eig(res.pca): Visualize the eigenvalues
#get_pca_ind(res.pca), get_pca_var(res.pca): Extract the results for individuals and variables, respectively.
#fviz_pca_ind(res.pca), fviz_pca_var(res.pca): Visualize the results individuals and variables, respectively.
#fviz_pca_biplot(res.pca): Make a biplot of individuals and variables.

eig.val <- get_eigenvalue(res.pca)
eig.val
##       eigenvalue variance.percent cumulative.variance.percent
## Dim.1 2.18880975        54.720244                    54.72024
## Dim.2 1.07192119        26.798030                    81.51827
## Dim.3 0.67915089        16.978772                    98.49705
## Dim.4 0.06011817         1.502954                   100.00000
fviz_eig(res.pca, addlabels = TRUE, ylim = c(0, 50))

var <- get_pca_var(res.pca)
#var$coord: coordinates of variables to create a scatter plot
#var$cos2: represents the quality of representation for variables on the factor map. It’s calculated as the squared coordinates: var.cos2 = var.coord * var.coord.
#var$contrib: contains the contributions (in percentage) of the variables to the principal components. 
#The contribution of a variable (var) to a given principal component is (in percentage) : (var.cos2 * 100) / (total cos2 of the component).
var
## Principal Component Analysis Results for variables
##  ===================================================
##   Name       Description                                    
## 1 "$coord"   "Coordinates for the variables"                
## 2 "$cor"     "Correlations between variables and dimensions"
## 3 "$cos2"    "Cos2 for the variables"                       
## 4 "$contrib" "contributions of the variables"
# Coordinates
head(var$coord)
##                    Dim.1       Dim.2       Dim.3        Dim.4
## SeniorCitizen  0.1325660  0.91799555  0.37377113 -0.002359512
## tenure         0.8358793 -0.32338157  0.42115076  0.139147812
## MonthlyCharges 0.7184745  0.33934293 -0.60093743  0.086688764
## TotalCharges   0.9779244 -0.09734524  0.03085889 -0.182306182
# Cos2: quality on the factore map
head(var$cos2)
##                     Dim.1       Dim.2       Dim.3        Dim.4
## SeniorCitizen  0.01757375 0.842715829 0.139704855 5.567297e-06
## tenure         0.69869428 0.104575639 0.177367965 1.936211e-02
## MonthlyCharges 0.51620563 0.115153626 0.361125798 7.514942e-03
## TotalCharges   0.95633609 0.009476097 0.000952271 3.323554e-02
# Contributions to the principal components
head(var$contrib)
##                     Dim.1      Dim.2      Dim.3       Dim.4
## SeniorCitizen   0.8028906 78.6173309 20.5705179  0.00926059
## tenure         31.9211974  9.7559075 26.1161352 32.20675989
## MonthlyCharges 23.5838511 10.7427325 53.1731319 12.50028450
## TotalCharges   43.6920608  0.8840292  0.1402149 55.28369502
#The plot Below is also known as variable correlation plots. It shows the relationships between all variables. It can be interpreted as follow:

#Positively correlated variables are grouped together.
#Negatively correlated variables are positioned on opposite sides of the plot origin (opposed quadrants).
#The distance between variables and the origin measures the quality of the variables on the factor map. 
#Variables that are away from the origin are well represented on the factor map.

# Correlation circle
fviz_pca_var(res.pca, col.var = "black")

# Quality of representation


corrplot(var$cos2, is.corr=FALSE)

# Total cos2 of variables on Dim.1 and Dim.2
#A high cos2 indicates a good representation of the variable on the principal component. 
#In this case the variable is positioned close to the circumference of the correlation circle.
#A low cos2 indicates that the variable is not perfectly represented by the PCs. 
#In this case the variable is close to the center of the circle.

fviz_cos2(res.pca, choice = "var", axes = 1:2)

fviz_pca_var(res.pca, col.var = "cos2",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"), 
             repel = TRUE # Avoid text overlapping
             )

# Change the transparency by cos2 values
fviz_pca_var(res.pca, alpha.var = "cos2")

corrplot(var$contrib, is.corr=FALSE)

# Contributions of variables to PC1
fviz_contrib(res.pca, choice = "var", axes = 1, top = 10)

# Contributions of variables to PC2
fviz_contrib(res.pca, choice = "var", axes = 2, top = 10)

fviz_pca_var(res.pca, col.var = "contrib",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07")
             )

fviz_pca_var(res.pca, alpha.var = "contrib")

fviz_pca_ind(res.pca,
             geom.ind = "point", # show points only (nbut not "text")
             col.ind = telecom$Churn, # color by groups
             palette = c("#00AFBB", "#E7B800", "#FC4E07"),
             addEllipses = TRUE, # Concentration ellipses
             legend.title = "Groups"
             )

# Description of PC

res.desc <- dimdesc(res.pca, axes = c(1,2,3,4), proba = 0.05)
# Description of dimension 1
res.desc$Dim.1
## 
## Link between the variable and the continuous variables (R-square)
## =================================================================================
##                correlation       p.value
## TotalCharges     0.9779244  0.000000e+00
## tenure           0.8358793 5.825435e-262
## MonthlyCharges   0.7184745 2.233972e-159
## SeniorCitizen    0.1325660  2.630198e-05
res.desc$Dim.2
## 
## Link between the variable and the continuous variables (R-square)
## =================================================================================
##                correlation      p.value
## SeniorCitizen   0.91799555 0.000000e+00
## MonthlyCharges  0.33934293 2.411027e-28
## TotalCharges   -0.09734524 2.068245e-03
## tenure         -0.32338157 9.452175e-26
res.desc$Dim.3
## 
## Link between the variable and the continuous variables (R-square)
## =================================================================================
##                correlation      p.value
## tenure           0.4211508 3.206661e-44
## SeniorCitizen    0.3737711 1.774212e-34
## MonthlyCharges  -0.6009374 4.192192e-99
res.desc$Dim.4
## 
## Link between the variable and the continuous variables (R-square)
## =================================================================================
##                correlation      p.value
## tenure          0.13914781 1.014671e-05
## MonthlyCharges  0.08668876 6.112200e-03
## TotalCharges   -0.18230618 6.489357e-09
res.desc$Dim.5
## NULL
# Graph of Indiviuals
ind <- get_pca_ind(res.pca)
ind
## Principal Component Analysis Results for individuals
##  ===================================================
##   Name       Description                       
## 1 "$coord"   "Coordinates for the individuals" 
## 2 "$cos2"    "Cos2 for the individuals"        
## 3 "$contrib" "contributions of the individuals"
## Principal Component Analysis Results for individuals
##  ===================================================
##   Name       Description                       
## 1 "$coord"   "Coordinates for the individuals" 
## 2 "$cos2"    "Cos2 for the individuals"        
## 3 "$contrib" "contributions of the individuals"
#To get access to the different components, use this:

# Coordinates of individuals
head(ind$coord)
##        Dim.1       Dim.2       Dim.3       Dim.4
## 1 -2.0164770 -0.30650514  0.01205626 -0.39542673
## 2 -0.2863112 -0.50159508  0.06162007  0.07534611
## 3 -1.5811368 -0.05917176 -0.55150822 -0.11415105
## 4 -0.2877582 -0.79879423  0.64491878  0.16971001
## 5 -1.2948089  0.12379343 -0.96183626  0.07099114
## 6 -0.4942924  0.33811617 -1.53341832  0.33310630
# Quality of individuals
head(ind$cos2)
##        Dim.1       Dim.2        Dim.3       Dim.4
## 1 0.94197953 0.021763587 3.367285e-05 0.036223214
## 2 0.23895965 0.733422844 1.106859e-02 0.016548918
## 3 0.88630674 0.001241293 1.078324e-01 0.004619607
## 4 0.07104055 0.547420153 3.568297e-01 0.024709609
## 5 0.63940313 0.005844651 3.528301e-01 0.001922081
## 6 0.08660999 0.040525839 8.335304e-01 0.039333792
# Contributions of individuals
head(ind$contrib)
##         Dim.1        Dim.2        Dim.3       Dim.4
## 1 0.185957210 0.0087729810 2.142363e-05 0.260351942
## 2 0.003748894 0.0234951487 5.596451e-04 0.009452583
## 3 0.114331366 0.0003269645 4.483036e-02 0.021696448
## 4 0.003786883 0.0595856249 6.130251e-02 0.047956084
## 5 0.076672189 0.0014310897 1.363548e-01 0.008391452
## 6 0.011173631 0.0106758763 3.465689e-01 0.184754261
fviz_pca_ind(res.pca)

fviz_pca_ind(res.pca, col.ind = "cos2", 
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE # Avoid text overlapping (slow if many points)
             )

fviz_pca_ind(res.pca, pointsize = "cos2", 
             pointshape = 21, fill = "#E7B800",
             repel = TRUE # Avoid text overlapping (slow if many points)
             )

fviz_pca_ind(res.pca, col.ind = "cos2", pointsize = "cos2",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE # Avoid text overlapping (slow if many points)
             )

fviz_cos2(res.pca, choice = "ind")

# Total contribution on PC1 and PC2
fviz_contrib(res.pca, choice = "ind", axes = 1:2)

# Create a random continuous variable of length 23,
# Same length as the number of active individuals in the PCA
set.seed(123)
my.cont.var <- rnorm(49)